Homepage > Publications

Publications

© All material accessible through this page is copyright by Yehuda Pinchover and his coauthors and by the corresponding publishers. Permission is granted for fair use in personal, noncommercial, and academic projects.

For a complete list of my publications see my vitae.

the reviews of my papers in “MathSciNet” of the American Mathematical Society

Here are links to some of my mathematical books.

Books

  1. Y. Pinchover and J. Rubinstein, “An Introduction to Partial Differential Equations“, 400 pp., Cambridge University Press, 2005. Errata
  2. Y. Pinchover and J. Rubinstein, “Introduction to Partial Differential Equations”, (in Hebrew), Technion, 312 pp., (First Edition 2001, Enlarged Second Edition, 2003, Enlarged Third Edition, 2006) Fourth Edition 2011. Errata
  3. M. Entov, Y. Pinchover and M. Sageev (Editors), “Geometry, Spectral Theory, Groups, and Dynamics: Proceedings in Memory of Robert Brooks”, Contemporary Mathematics, 300 pp., American Mathematical Society, Providence, RI, 2005.

    Articles

  4. Y. Pinchover, Sur les solutions positives d’equations elliptiques et paraboliques dans Rn , C. R. Acad. Sc. Paris 302 I (1986), 447-450.
  5. Y. Pinchover, Representation theorems for positive solutions of parabolic equations, Proc. Amer. Math. Soc. 104 (1988), 507-515.
  6. Y. Pinchover, On positive solutions of second-order elliptic equations, stability results and classification, Duke Math. J. 57 (1988), 955-980.
  7. Y. Pinchover, On positive solutions of elliptic equations with periodic coefficients in unbounded domains, in: “Maximum Principles and Eigenvalue Problems in Partial Differential Equations (Knoxville, TN, 1987)”, ed. P. W. Schaefer, Pitman Res. Notes in Math. 175, Longman Sci. Tech., London, 1988, 218-230.
  8. Y. Pinchover, Criticality and ground states for second-order elliptic equations, J. Differential Equations 80 (1989), 237-250.
  9. Y. Pinchover, On criticality and ground states of second-order elliptic equations II, J. Differential Equations 87 (1990), 353-364.
  10. Y. Pinchover, Large scale properties of multiparameter oscillation problems, Comm. Partial Differential Equations 15 (1990), 647-673.
  11. Y. Pinchover, Large time behavior of the heat kernel and the behavior of the Green function near criticality for nonsymmetric elliptic operators, J. Functional Analysis 104 (1992), 54-70.
  12. Y. Pinchover, On the equivalence of Green functions of second order elliptic equations in Rn, Differential and Integral Equations 5 (1992), 481-493.
  13. R. D. Nussbaum and Y. Pinchover, On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications, J. Anal. Math. 59 (1992), 161-177.
  14. V. Lin and Y. Pinchover, Manifolds with group actions and elliptic operators, Memoirs Amer. Math. Soc. Vol. 112, No. 540 (1994), 1-78.
  15. Y. Pinchover, On positive Liouville theorems and asymptotic behavior of solutions of Fuchsian type elliptic operators, Ann. Inst. H. Poincare. Anal. Non Lineaire 11 (1994), 313-341.
  16. Y. Pinchover, Nonexistence of any λ0-invariant positive harmonic function, a counter example to Stroock’s conjecture, Comm. Partial Differential Equations 20 (1995), 1831-1846.
  17. Y. Pinchover, On the localization of binding for Schrödinger operators and its extension to elliptic operators, J. Anal. Math. 66 (1995), 57-83.
  18. Y. Pinchover, On positivity, criticality and spectral radius of the shuttle operator for elliptic operators, Duke Math. J. 85 (1996), 431-445.
  19. Y. Pinchover, Binding of Schrödinger particles through conspiracy of potential wells in R4, in: Progress in Partial Differential Equations: the Metz Surveys 4, eds. M. Chipot and I. Shafrir (Pitman Research Notes in Mathematics 345), Longman Press, London (1996), 118-133.
  20. Y. Pinchover, On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients, Math. Zeitschrift 233 (1996), 569-586.
  21. Y. Pinchover, Generalized principal eigenvalues for indefinite-weight elliptic problems, C. R. Acad. Sc. Paris 326 (1998), 697-702.
  22. M. Marcus, V. J. Mizel and Y. Pinchover, On the best constant for Hardy’s inequality in Rn, Trans. Amer. Math. Soc. 350 (1998), 3237-3255.
  23. Y. Pinchover, On principal eigenvalues for indefinite-weight elliptic problems, in: Spectral and Scattering Theory, ed A.G. Ramm, Plenum, New York, (1998), 77-87.
  24. Y. Pinchover, Maximum and anti-maximum principles and eigenfunctions estimates via perturbation theory of positive solutions of elliptic equations, Math. Ann. 314 (1999), 555-590.
  25. Y. Pinchover, On the maximum and anti-maximum principles, in: “Differential Equations and Mathematical Physics (Birmingham, AL, 1999)”, 323-338, R. Weikard and G. Weinstein eds., AMS/IP Studies in Adv. Math., Vol. 16, Amer. Math. Soc., Providence, RI, 2000.
  26. P. Kuchment and Y. Pinchover, Integral representations and Liouville theorems for solutions of periodic elliptic equations, J. Functional Analysis 181 (2001), 402-446. arXiv: 0007051
  27. Y. Pinchover, Anti-maximum principles for indefinite-weight elliptic problems, Comm. Partial Differential Equations 26 (2001), 1861-1877.
  28. Y. Pinchover and T. Saadon, On positivity of solutions of degenerate boundary value problems for second-order elliptic equations, Israel J. Math. 132 (2002), 125-168.
  29. Y. Pinchover and T. Saadon (Suez), Degenerate elliptic mixed boundary value problems: positive solutions, principal eigenvalue, Green function, and criticality theory, in: “Progress in Analysis, Proceedings of the 3rd ISAAC Congress”, eds. H. G. W. Begehr, R. P. Gilbert and M. W. Wong, World Scientific, New Jersey, 2003, 623-634.
  30. Y. Pinchover, Large time behavior of the heat kernel, J. Functional Analysis 206 (2004), 191-209, arXiv: 0206281.
  31. Y. Pinchover and K. Tintarev, Existence of minimizers for Schrödinger operators under domain perturbations with application to Hardy’s inequality, Indiana Univ. Math. J. 54 (2005), 1061-1074, arXiv: 0410078.
  32. Y. Pinchover and K. Tintarev, A ground state alternative for singular Schrödinger operators, J. Functional Analysis, 230 (2006), 65-77. arXiv: 0411658.
  33. P. Kuchment and Y. Pinchover, Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds, Trans. Amer. Math. Soc. 359 (2007), 5777-5815. arXiv: 0503010.
  34. Y. Pinchover, On Davies’ conjecture and strong ratio limit properties for the heat kernel, in “Potential Theory in Matsue”, Proceedings of the International Workshop on Potential Theory, 2004, ed. H. Aikawa, Advanced Studies in Pure Mathematics 44, Mathematical Society of Japan, Tokyo, 2006, 339-352. arXiv: 0504344.
  35. Y. Pinchover and K. Tintarev, Ground state alternative for p-Laplacian with potential term, Calc. Var. Partial Differential Equations 28 (2007), 179-201. arXiv: 0511039.
  36. Y. Pinchover, Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations, in “Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday”, eds. F. Gesztesy, et al., Proceedings of Symposia in Pure Mathematics 76, American Mathematical Society, Providence, RI, 2007, 329-356. arXiv: 0512430.
  37. Y. Pinchover, A Liouville-type theorem for Schrödinger operators, Comm. Math. Phys. 272 (2007), 75-84. arXiv: 0512431.
  38. Y. Pinchover, A. Tertikas and K. Tintarev, A Liouville-type theorem for the p-Laplacian with potential term, Ann. Inst. H. Poincare-Anal. Non Lineaire 25 (2008), 357-368. arXiv: 0609126.
  39. Y. Pinchover, G.Wolansky and D. Zelig, Spectral properties of Schrödinger operators defined on N-dimensional infinite trees, Israel J. Math., 165 (2008), 281-328. arXiv: 0608716.
  40. Y. Pinchover and K. Tintarev, On positive solutions of minimal growth for singular p-Laplacian with potential term, Advanced Nonlinear Studies 8 (2008), 213-234. arXiv: 0707.2169.
  41. Y. Pinchover and K. Tintarev, On the Hardy-Sobolev-Maz’ya inequality and its generalizations, in “Sobolev Spaces in Mathematics I: Sobolev Type Inequalities”, ed. V. Maz’ya, International Mathematical Series 8, Springer, 2009, 281-297. arXiv: 1003.2374.
  42. Y. Pinchover, Book Review: The maximum principle, by P. Pucci and J. Serrin [Progress in Nonlinear Differential Equations and their Applications 73, Birkhauser Verlag, Basel, 2007], Bull. Amer. Math. Soc. 46 (2009), 499–504.
  43. Y. Pinchover and K. Tintarev, On positive solutions of p-Laplacian-type equations, in: “Analysis, Partial Differential Equations and Applications – The Vladimir Maz’ya Anniversary Volume”, eds. A. Cialdea et al., Operator Theory: Advances and Applications, Vol. 193, Birkauser Verlag, Basel, 2009, 245-268. 0901.0847.
  44. M. Fraas, D. Krejcirik and Y. Pinchover, On some strong ratio limit theorems for heat kernels, Discrete Contin. Dyn. Syst. Ser. A, a special special volume dedicated to Louis Nirenberg on the occasion of his 85th birthday, 28 (2010), 495–509. arXiv: 0912.4337.
  45. M. Fraas and Y. Pinchover, Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential, Confluentes Mathematici 3 (2011) 291-323. arXiv: 1003.5452.
  46. B. Devyver, M. Fraas and Y. Pinchover, Optimal Hardy-type inequalities for elliptic operators, C. R. Acad. Sc. Paris 350 (2012), 475-479. PDF
  47. M. Fraas and Y. Pinchover, Isolated singularities of positive solutions of p-Laplacian type equations in Rd, J. Differential Equations 254 (2013), 1097-1119. arXiv: 1008.3873.
  48. Y. Pinchover, Some aspects of large time behavior of the heat kernel: an overview with perspectives, in “Mathematical Physics, Spectral Theory and Stochastic Analysis”, eds. M. Demuth and W. Kirsch, Operator Theory: Advances and Applications, Vol. 232, Springer Verlag, Basel, 2013, 299-339. arXiv: 1209.0665.
  49. B. Devyver, M. Fraas and Y. Pinchover, Optimal Hardy Weight for Second-Order Elliptic Operator: an answer to a problem of Agmon, J. Functional Analysis 266 (2014), 4422-4489. arXiv: 1208.2342.
  50. G. Grillo, H. Kovarik and Y. Pinchover, Sharp two-sided heat kernel estimates of twisted tubes and applications, Arch. Rational Mech. Anal. 213 (2014). 215–243. arXiv: 1105.0842.
  51. Y. Pinchover, Commentary on James Serrin’s papers concerning the theory of the Dirichlet problem, in: James Serrin. Selected Papers, Vol. 1, P. Pucci, V.D. Radulescu, and H. Weinberger (Eds.), Birkhauser Verlag, Basel, 2014, 117–119.
  52. B. Devyver, Y. Pinchover, and G. Psaradakis, On optimal Hardy inequalities in cones, Bruno Pini Math. Anal. Semin. 2014 (2014), 67-82, Univ. Bologna, Alma Mater Stud., Bologna.
  53. Y. Pinchover, and N. Regev, Criticality theory of half-linear equations with the (p,A)-Laplacian, Nonlinear Anal. 119 (2015), 295-314. arXiv: 1409.3346.
  54. B. Devyver, and Y. Pinchover, Optimal Lp Hardy-type inequalities, Ann. Inst. H. Poincare. Anal. Non Lineaire 33 (2016), 93–118. arXiv: 1312.6235.
  55. Y. Pinchover, and G. Psaradakis, On positive solutions of the (p,A)-Laplacian with a potential in Morrey space, Anal. PDE 9 (2016), 1317-1358. arXiv: 1508.04961.
  56. A.E. Kogoj, Y. Pinchover, and S. Polidoro, On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators, J. Evol. Equ. 16 (2016), 905-943. arXiv: 1404.0288.
  57. Y. Pinchover, On the boundedness and compactness of weighted Green operators of second-order elliptic operators, “Functional Analysis and Operator Theory for Quantum Physics”, Pavel Exner Anniversary Volume, eds. J. Dittrich, H.Kovarik, and A. Laptev,  EMS Publishing House, 2017, 459-490. arXiv: 1601.01464.
  58. B. Devyver, Y. Pinchover, and G. Psaradakis, Optimal Hardy inequalities in cones, Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), 89-124. arXiv: 1502.05205.
  59. D. Ganguly, and Y. Pinchover, On Green functions of second-order elliptic operators on Riemannian manifolds: The critical case, J.Functional Analysis 274 (2018), 2700-2724. arXiv: 1609.08200.
  60.  M. Keller, Y. Pinchover, and F. Pogorzelski, Optimal Hardy inequalities for Schrödinger operators on graphs, Comm. Math. Phys. 358 (2018), 767-790. arXiv: 1612.04051.
  61. M. Keller, Y. Pinchover, and F. Pogorzelski, An improved discrete Hardy inequality, Amer. Math. Monthly 125 (2018), 347-350. arXiv: 1612.05913.
  62. P. D. Lamberti, and Y. Pinchover, Lp Hardy inequality on C1,α domains, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), 1135-1159. arXiv: 1611.00563
  63. H. Kovarik, Y. Pinchover, On minimal decay at infinity of Hardy-weights,  Commun. Contemp. Math. 22 (2020), 1950046. arXiv: 1812.01849.
  64. M. Keller, Y. Pinchover, and F. Pogorzelski, Criticality theory for Schrödinger operators on graphs, J. Spectr. Theory 10 (2020), 73–114. arXiv: 1708.09664.
  65. D. Ganguly, and Y. Pinchover,  On the equivalence of heat kernels of second-order parabolic operators, J. Anal. Math. 140(2) (2020), 549-589.  arXiv: 1606.08601.
  66. E. Berchio, G. Grillo, D. Ganguly, and Y. Pinchover, An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds, Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), 1699-1736.
  67. S. Beckus, and Y. Pinchover, Shnol-type theorem for the Agmon ground state, J. Spectr. Theory 10 (2020), 355-377. arXiv: 1706.04869.
  68. D. Ganguly, and Y. Pinchover, Some new aspects of perturbation theory of positive solutions of second-order linear elliptic equations, published in a special issue dedicated to the memory of A. I. Volpert, Pure Appl. Funct. Anal. 5 (2020), 295-319. arXiv: 1812.03450.
  69. Y. Pinchover, and I. Versano, On families of optimal Hardy-weights for linear second-order elliptic operators, J. Functional Analysis, 278 (2020) 108428, arXiv: 1909.12512.
  70. M. Keller, Y. Pinchover, and F. Pogorzelski, Critical Hardy inequalities on manifolds and graphs,  in “Analysis and Geometry on Graphs and Manifolds”, eds. R.K. Wojciechowski et al, London Mathematical Society Lecture Notes Series (461), Cambridge University Press, Cambridge, 2020, 172-202.
  71. Ratan Kr. Giri, and Y. Pinchover, Positive Liouville theorem and asymptotic behaviour for (p,A)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space, appeared in a topical collection: Harmonic Analysis and PDE dedicated to the 80th birthday of  Vladimir Maz’ya,  Anal. Math. Phys. 10, Article number: 67 (2020), arXiv: 2007.02254.
  72. M. Keller, Y. Pinchover, and F. Pogorzelski, From Hardy to Rellich inequalities on graphs, Proc. Lond. Math. Soc. (3) 122 (2021) 458-477,  arXiv: 1909.02286.
  73. Y. Pinchover, Book Review: Invitation to partial differential equations, by M. Shubin, Edited by M. Braverman, R. McOwen, and P. Topalov. [Graduate Studies in Mathematics  205, American Mathematical Society, Providence, RI, 2020], Bull. Amer. Math. Soc. 59 (2022), 139-143.
  74. D. Goel, Y. Pinchover, and G. Psaradakis, On weighted Lp-Hardy inequality on domains in Rn, in: Special Issue on Analysis and PDE Dedicated to Professor Shmuel Agmon, Pure Appl. Funct. Anal. 7 (2022), 1025-1033. arXiv: 2012.12860.
  75. D. Ganguly, Y. Pinchover, and P. Roychowdhury, Stochastic completeness and L1-Liouville property for second-order elliptic operators, in: “Partial Differential Equations and Semigroups in Applied Analysis”, special volume dedicated to J.A. Goldstein in honor of his 80th birthday, Discrete Contin. Dyn. Syst. Ser. S., doi: 10.3934/dcdss.2022138 (2022). 15pp. arXiv: 2203.06493.
  76. Y. Pinchover, and I. Versano, On criticality theory for elliptic mixed boundary value problems in divergence form, Commun. Contemp. Math. Vol.25, (2023),  2250051  (48 pp.), arXiv: 2008.03699.
  77. Ratan Kr. Giri, and Y. Pinchover, Positive solutions of quasilinear elliptic equations with Fuchsian potentials in Wolff class, Milan J. Math. 91 (2023), 59-96. arXiv: 2204.08061
  78. Y. Hou, Y. Pinchover, and A. Rasila, Positive solutions of the A-Laplace equation with a potential, Potential Anal. 60 (2024), 721-758. arXiv: 2112.01755.
  79. Y. Pinchover, and I. Versano, Optimal Hardy-weights for elliptic operators with mixed boundary conditions, Mathematika 69 (2023), 1221-1241. arXiv: 2103.13979
  80. U. Das, and Y. Pinchover, The space of Hardy-weights for quasilinear equations: Maz’ya-type characterization and sufficient conditions for existence of minimizers, J. Anal. Math. (2023), 36 pp.. DOI10.1007/s11854-023-0318-8 arXiv: 2202.12324.
  81. U. Das, Y. Pinchover, and B. Devyver, On existence of minimizers for weighted Lp-Hardy inequalities on C1,α -domains with compact boundary. arXiv: 2303.03527
  82. U. Das, and Y. Pinchover, A lower bound for the weighted-Hardy constant for domains satisfying a uniform exterior cone condition. arXiv: 2307.01372