Abstract
We study the existence and uniqueness for weak solutions to some classes of anisotropic elliptic Dirichlet problems with data belonging to the natural dual space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alvino A., Betta M.F., Mercaldo A.: Comparison principle for some classes of nonlinear elliptic equations, J. Differential Equations 249, 3279–3290 (2010)
Antontsev S., Chipot M.: Anisotropic equations: uniqueness and existence results. Differential Integral Equations 21, 401–419 (2008)
Betta M.F. et al.: Uniqueness results for nonlinear elliptic equations with a lower order term. Nonlinear Anal 63, 153–170 (2005)
Boccardo L., Gallouet T., Marcellini P.: Anisotropic equations in L 1. Differential Integral Equations 9, 209–212 (1996)
L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal. 19 (1992), 581–597.
G. Bottaro and M. Marina, Problema di Dirichlet per equazioni ellittiche di tipo variazionale su insiemi non limitati, Boll. Un. Mat. Ital. 8 (1973), 46–56.
Cianchi A.: Symmetrization in anisotropic elliptic problems, Comm. Partial Differential Equations 32, 693–717 (2007)
T. Del Vecchio and M. M. Porzio, Existence results for a class of non-coercive Dirichlet problems, Ricerche Mat. 44 (1995), 421–438 (1996).
T. Del Vecchio and M. R. Posteraro, An existence result for nonlinear and noncoercive problems, Nonlinear Anal. 31 (1998), 191–206.
Di Castro A.: Existence and regularity results for anisotropic elliptic problems. Adv.Nonlinear Stud. 9, 367–393 (2009)
R. Di Nardo, F. Feo, and O. Guibé, Existence result for nonlinear parabolic equations with lower order terms, Anal. Appl. 9 (2011), 161–186
R. Di Nardo, F. Feo, and O. Guibé, Uniqueness result for nonlinear anisotropic elliptic equations. Adv. Differential Equations 18 (2013), 433–458.
I. Fragalà, F. Gazzola, and B. Kawohl, Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004), 715–734.
O. Guibé and A. Mercaldo, Existence of renormalized solutions to nonlinear elliptic equations with two lower order terms and measure data, Trans. Amer. Math. Soc. 360 (2008), 643–669.
O. Guibé and A. Mercaldo, Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms, Commun. Pure Appl. Anal. 7 (2008), 163–192.
Li F.: Anisotropic elliptic equations in Lˆm. J. Convex Anal. 8, 417–422 (2001)
J. Leray and J. L. Lions, Quelques résultats de Višik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder (French) - Bull. Soc. Math. France 93 (1965), 97–107.
Porretta A.: On the comparison principle for p -Laplace type operators with first order terms. On the notions of solution to nonlinear elliptic problems: results and developments, Quad. Mat. 23, 459–497 (2008)
Troisi M.: Teoremi di inclusione per spazi di Sobolev non isotropi. Ricerche Mat. 18, 3–24 (1969)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Di Nardo, R., Feo, F. Existence and uniqueness for nonlinear anisotropic elliptic equations. Arch. Math. 102, 141–153 (2014). https://doi.org/10.1007/s00013-014-0611-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-014-0611-y