Growth conditions and regularity, an optimal local boundedness result

DOI10.1142/S0219199720500297zbMath1458.49009arXiv1911.12822OpenAlexW3036959523MaRDI QIDQ5152078

Mathias Schäffner, Jonas Hirsch

Publication date: 18 February 2021

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.12822

zbMATH Keywords

local boundedness\((p,q)\)-growth conditions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (22)

Local boundedness for solutions of a class of nonlinear elliptic systems ⋮ Higher integrability for variational integrals with non-standard growth ⋮ Quasiconvexity and partial regularity via nonlinear potentials ⋮ Optimal gradient estimates for multi-phase integrals ⋮ Borderline Lipschitz regularity for bounded minimizers of functionals with \((p,q)\)-growth ⋮ Global higher integrability for minimisers of convex functionals with \((p,q)\)-growth ⋮ Nonuniformly elliptic Schauder theory ⋮ Local boundedness under nonstandard growth conditions ⋮ Lipschitz bounds for integral functionals with \((p,q)\)-growth conditions ⋮ Boundary regularity results for minimisers of convex functionals with \((p, q)\)-growth ⋮ The Sobolev class where a weak solution is a local minimizer ⋮ Local boundedness of weak solutions to elliptic equations with \(p, q\)-growth ⋮ Local boundedness for \(p \)-Laplacian with degenerate coefficients ⋮ Singular multiple integrals and nonlinear potentials ⋮ Unnamed Item ⋮ Interpolative gap bounds for nonautonomous integrals ⋮ Interpolative gap bounds for nonautonomous integrals ⋮ Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems ⋮ Lipschitz bounds and nonautonomous integrals ⋮ A local boundedness result for a class of obstacle problems with non-standard growth conditions ⋮ Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence ⋮ Boundary regularity for manifold constrained p(x)‐harmonic maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local boundedness of minimizers with limit growth conditions
• Bounded minimisers of double phase variational integrals
• Higher differentiability of minimizers of convex variational integrals
• Regularity for elliptic equations with general growth conditions
• Local boundedness of minimizers in a limit case
• An introduction to Sobolev spaces and interpolation spaces
• Regularity of minima: an invitation to the dark side of the calculus of variations.
• Growth conditions and regularity. A counterexample
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• On the regularity of the minima of variational integrals
• \(C^1\) regularity of orthotropic \(p\)-harmonic functions in the plane
• Regularity for general functionals with double phase
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• On the regularity of minima of non-autonomous functionals
• Quenched invariance principle for random walks among random degenerate conductances
• Regularity for double phase variational problems
• On the regularity of generalized solutions of linear, non-uniformly elliptic equations
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Elliptic Partial Differential Equations of Second Order
• Some remarks on the regularity of minima of anisotropic integrals
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations
• Lipschitz Bounds and Nonuniform Ellipticity
• Function Spaces

This page was built for publication: Growth conditions and regularity, an optimal local boundedness result