On the integrability of solutions of nonlinear elliptic equations with right-hand sides in classes close to \(L^ 1\).

DOI10.1023/A:1012343728148zbMath1140.35444OpenAlexW319741011MaRDI QIDQ1809997

Alexander A. Kovalevsky

Publication date: 15 June 2003

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1012343728148

zbMATH Keywords

Young's inequalityFatou lemmaentropy and weak solutions of the Dirichlet problemintegrability of solutions of nonlinear elliptic equations

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45)

Related Items

Integrability properties of functions with a given behavior of distribution functions and some applications, Summability of solutions of the Dirichlet problem for nonlinear elliptic equations with right-hand side in classes close to \(L^1\), Regularity results for solutions of nonlinear elliptic equations with \(L^{1,\lambda }\) data, Regularity results for the gradient of solutions linear elliptic equations with \(L^{1,\lambda}\) data, Summability of solutions of the Dirichlet problem for nonlinear elliptic equations with right-hand side in logarithmic classes close to \(L^1\), Summability of solutions of some degenerate nonlinear elliptic fourth-order equations, On the sets of \(L^\infty \)-regularity of solutions for a class of degenerate nonlinear problems with slightly regular data, General conditions for limit summability of solutions of nonlinear elliptic equations with \(L^1\)-data, On limit summability of solutions for a class of degenerate nonlinear high-order equations withL¹-data, Summability of Solutions of Dirichlet Problem for a Class of Degenerate Nonlinear High-order Equations, On improvement of summability properties of solutions of some degenerate nonlinear fourth-order equations