Besov regularity of solutions to the \(p\)-Poisson equation

DOI10.1016/j.na.2015.10.015zbMath1330.35189arXiv1408.4271OpenAlexW2962896047MaRDI QIDQ898374

Benjamin Scharf, Markus Weimar, Lars Diening, Christoph Hartmann, Stephan Dahlke

Publication date: 8 December 2015

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

Full work available at URL: https://arxiv.org/abs/1408.4271

zbMATH Keywords

waveletsBesov spacesHölder spacesregularity of solutions\(p\)-Poisson equationnonlinear and adaptive approximation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stability in context of PDEs (35B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Numerical methods for wavelets (65T60) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (20)

Almost diagonal matrices and Besov-type spaces based on wavelet expansions ⋮ Regularity estimates for the parabolic \(p (x, t)\)-Laplacian equation in Besov spaces ⋮ Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type ⋮ Rate-optimal sparse approximation of compact break-of-scale embeddings ⋮ Besov estimates for weak solutions of a class of quasilinear parabolic equations with general growth ⋮ Higher differentiability for solutions of stationary p‐Stokes systems ⋮ On the lack of interior regularity of the p‐Poisson problem with p>2 ⋮ Besov regularity for operator equations on patchwise smooth manifolds ⋮ Fractional higher differentiability for solutions of stationary Stokes and Navier-Stokes systems with Orlicz growth ⋮ Boundary regularity results for minimisers of convex functionals with \((p, q)\)-growth ⋮ Besov regularity of parabolic and hyperbolic PDEs ⋮ Besov regularity of solutions to the \(p\)-Poisson equation in the vicinity of a vertex of a polygonal domain ⋮ Besov estimates for weak solutions of the parabolic \(p\)-Laplacian equations ⋮ On Besov regularity of solutions to nonlinear elliptic partial differential equations ⋮ Besov regularity estimates for the elliptic \(p(x)\)-Laplacian equation with the logarithmic growth ⋮ On the limit regularity in Sobolev and Besov scales related to approximation theory ⋮ A \(hk\) mortar spectral element method for the \(p\)-Laplacian equation ⋮ Higher Order Regularity Shifts for the p-Poisson Problem ⋮ Higher order Calderón-Zygmund estimates for the \(p\)-Laplace equation ⋮ Besov estimates for the weak solutions of a class of quasilinear elliptic equations

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