On the modulus of continuity of solutions to the \(n\)-Laplace equation

DOI10.1007/BF03377364zbMath1378.35112MaRDI QIDQ1691799

Carlo Sbordone, Angela Alberico, Andrea Cianchi

Publication date: 25 January 2018

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

zbMATH Keywords

Sobolev embeddingsmodulus of continuityOrlicz spacesnonlinear elliptic equationscontinuity of solutionsclassical Lorentz spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Nonlinear elliptic equations (35J60)

Related Items (3)

Pointwise estimates of solutions to \(2 m\)-order quasilinear elliptic equations with \(m(p, q)\) growth via Wolff potentials ⋮ Continuity properties of solutions to the \(p\)-Laplace system ⋮ On the generalized \(\mathfrak{U}_{m, p}^f\) classes of De Giorgi-ladyzhenskaya-ural'tseva and pointwise estimates of solutions to high-order elliptic equations via Wolff potentials

Cites Work

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• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Discretization and anti-discretization of rearrangement-invariant norms
• Regularity properties of solutions of elliptic equations in \(\mathbb{R}^ 2\) in limit cases
• Continuity properties of minimizers of integral functionals in a limit case
• Sharp regularity for general Poisson equations with borderline sources
• Linear potentials in nonlinear potential theory
• Optimal summability of solutions to nonlinear elliptic problems
• On embeddings between classical Lorentz spaces
• Continuity estimates for $n$-harmonic equations

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