Form estimates for the 𝑝(𝑥)-Laplacean

DOI10.1090/S0002-9939-07-08718-7zbMath1123.35032MaRDI QIDQ3432779

Walter Allegretto

Publication date: 18 April 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

unbounded domains\(P(x)\)-Laplacianeigenvalues of the \(p(x)\)-Laplacian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Nonlinear elliptic equations (35J60)

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Cites Work

• Unnamed Item
• Unnamed Item
• Lower bounds for the first eigenvalue of elliptic equations
• Principal eigenvalues and Sturm comparison via Picone's identity
• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
• A class of De Giorgi type and Hölder continuity
• A Picone's identity for the p-Laplacian and applications
• Gradient estimates for thep(x)-Laplacean system
• Regularity results for a class of functionals with non-standard growth