Entropy solutions of Dirichlet problem for a class of degenerate anisotropic fourth-order equations with \(L ^{1}\)-right-hand sides
type: Item
instance of: scholarly article
title: Entropy solutions of Dirichlet problem for a class of degenerate anisotropic fourth-order equations with \(L ^{1}\)-right-hand sides
zbMATH Open document ID: 1012.35025
DOI: 10.1016/S0362-546X(01)00729-5
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: This paper is devoted to study entropy solutions of the Dirichlet problem for a class of degenerate anisotropic nonlinear elliptic fourth-order equations with \(L^1\)-right-hand sides. The authors introduce a notion of the entropy solution of the problem under consideration. Under some assumptions on the involved exponents and weighted functions related to the equations they obtain existence and uniqueness of a solution of this kind.
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1788031
zbMATH Keywords: existence and uniqueness results
author: Alexander A. Kovalevsky
author: Francesco Nicolosi
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q4851005
cites work: Existence and regularity of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms
cites work: Nonlinear Elliptic Equations with Right Hand Side Measures
cites work: Anisotropic equations in \(L^ 1\)
cites work: Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data
cites work: Entropy solutions of Dirichlet problem for a class of nonlinear elliptic fourth order equations with \(L_1\)-data
cites work: Entropy solutions of the Dirichlet problem for a class of non-linear elliptic fourth-order equations with right-hand sides in $ L^1$
cites work: Boundedness of solutions of variational inequalities with nonlinear degenerated elliptic operators of high order
cites work: Solvability of Dirichlet problem for a class of degenerate anisotropic equations with \(L^1\)-right-hand sides
cites work: Q5890172
cites work: Nirenberg-Gagliardo interpolation inequality and regularity of solutions of nonlinear higher order equations
cites work: Generalized solutions in a new type of sets for problems with measures as data
cites work: Q3207462
cites work: Teoremi di inclusione per spazi di Sobolev non isotropi
description: scientific article; zbMATH DE number 1788031