Optimal summability of solutions to nonlinear elliptic problems

DOI10.1016/j.na.2006.08.023zbMath1387.35282OpenAlexW2000362666MaRDI QIDQ2371171

Angela Alberico, Andrea Cianchi

Publication date: 29 June 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.08.023

zbMATH Keywords

Dirichlet problemsrearrangementselliptic equations\(p\)-LaplacianNeumann problemsLorentz spacespriori estimates

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) A priori estimates in context of PDEs (35B45)

Related Items

Gradient estimates below the duality exponent ⋮ Gradient regularity for quasilinear elliptic Dirichlet problems in the plane ⋮ Weighted inequalities for discrete iterated kernel operators ⋮ On the modulus of continuity of solutions to the \(n\)-Laplace equation ⋮ Continuity properties of solutions to the \(p\)-Laplace system ⋮ Optimal limiting embeddings for \(\Delta\)-reduced Sobolev spaces in \(L^1\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some observations on the regularity of the solutions of strongly nonlinear problems and applications
• Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces
• A Lorentz regularity theorem for solutions of nonlinear elliptic equations
• Discretization and anti-discretization of rearrangement-invariant norms
• Regularity properties of solutions of elliptic equations in \(\mathbb{R}^ 2\) in limit cases
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• On the summability of solutions of nonlinear elliptic equations in limit cases
• On embeddings between classical Lorentz spaces
• Elliptic equations on manifolds and isoperimetric inequalities
• Existence Results Via Regularity For Some Nonlinear Elliptic Problems
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions

This page was built for publication: Optimal summability of solutions to nonlinear elliptic problems