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Improved bounds for solutions of Φ-laplacians

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this short paper we prove a parametric version of the Harnack inequality for Φ-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.
Rocznik
Strony
765--777
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Khalifa University Department of Applied Mathematics and Sciences P.O. Box 127788, Abu Dhabi, United Arab Emirates
  • Universidad Austral de Chile Instituto de Ciencias Fisicas y Matematicas Campus Isla Tej a Valdivia, Chile
Bibliografia
  • [1] R.A. Adams, John J.J.F. Fournier, Sobolev Spaces, vol. 140, Pure and Applied Mathematics, 2nd ed., Elsevier B.V., Amsterdam, 2003.
  • [2] W. Arriagada, J. Huentutripay, A Harnack's inequality in Orlicz-Sobolev spaces, Studia Math. 243 (2018), 117-137.
  • [3] W. Arriagada, J. Huentutripay, Regularity, positivity and asymptotic vanishing of solutions of a (p-Laplacian, Anal. §tiin| Univ. "Ovidius" Constanta Ser. Mat. 25 (2017) 3, 59-72.
  • [4] H. Brezis, Analyse Fonctionnelle: Theorie et Applications, Masson, Paris, 1983.
  • [5] E. DiBenedetto, Partial Differential Equations, Cornerstones, Birkhauser Boston, Inc., Boston, MA, 2nd ed., 2010.
  • [6] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic System, Princeton Univ. Press, Princeton, New Jersey, 1983.
  • [7] D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag Germany, reprint of the 1998 edition, 2001.
  • [8] J.P. Gossez, Orlicz-Sobolev spaces and nonlinear elliptic boundary value problems, [in:] S. Fućik, A. Kufner (eds.), Nonlinear Analysis, Function Spaces and Applications, Proceedings of a Spring School held in Horni Bradlo, 1978, vol. 1, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1979. Teubner Texte zur Mathematik, 59-94.
  • [9] U. Kaufmann, I. Medri, One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign, Adv. Nonlinear Anal. 5 (2016), 251-259.
  • [10] M. Krasnosel'skii, J. Rutickii, Convex Functions and Orlicz Space, English translation P. Noordhoff Ltd., Groningen, 1961.
  • [11] G.M. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations, Comm. Partial Differential Equations 16 (1991) 2-3, 311-361.
  • [12] B. Maultsby, Uniqueness of solutions to singular p-Laplacian equations with subcritical nonlinearity, Adv. Nonlinear Anal. 6 (2017) 1, 37-59.
  • [13] J. Moser, On Harnack's theorem, for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591.
  • [14] V. Radulescu, Nonlinear elliptic equations with variable exponent: old and new, Nonlinear Anal. 121 (2015), 336-369.
  • [15] V. Radulescu, D. Repovs, Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis, Chapman & Hall/CRC Monographs and Research Notes in Mathematics, Taylor & Francis Group, Boca Raton FL, 2015.
  • [16] I.-L. Stancut;, I.D. Stircu, Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces, Opuscula Math. 36 (2016) 1, 81-101.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7213081b-8b98-438b-a6c7-764d162628b1
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