Boundary regularity for elliptic systems with \(p,q\)-growth

DOI10.1016/j.matpur.2021.12.004zbMath1487.35147OpenAlexW4200508051MaRDI QIDQ2668966

Frank Duzaar, Verena Bögelein, Paolo Marcellini, Christoph Scheven

Publication date: 9 March 2022

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2021.12.004

zbMATH Keywords

gradient estimatesboundary regularitynon-standard growthgeneral growth conditionselliptic equations and systems\(p, q\)-growth conditions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60) Variational methods for elliptic systems (35J50) A priori estimates in context of PDEs (35B45) Boundary value problems for second-order elliptic systems (35J57)

Related Items (8)

Asymptotic mean value properties for the elliptic and parabolic double phase equations ⋮ Boundary regularity for parabolic systems in convex domains ⋮ 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 ⋮ Gradient Hölder regularity for degenerate parabolic systems ⋮ Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary regularity of minimizers of \(p(x)\)-energy functionals
• Lipschitz estimates for systems with ellipticity conditions at infinity
• Bounded minimisers of double phase variational integrals
• Higher differentiability of minimizers of convex variational integrals
• A general regularity theorem for functionals with \(\varphi \)-growth
• Local Lipschitz regularity for degenerate elliptic systems
• Boundary regularity in variational problems
• Regularity for scalar integrals without structure conditions
• Everywhere-regularity for some quasilinear systems with a lack of ellipticity
• Boundary regularity and the Dirichlet problem for harmonic maps
• Nonlinear elliptic systems with general growth
• Everywhere regularity of functionals with \(\varphi \)-growth
• Lipschitz regularity for some asymptotically subquadratic problems
• Partial regularity for minimisers of certain functionals having nonquadratic growth
• Global regularity for almost minimizers of nonconvex variational problems
• Global Lipschitz regularity for almost minimizers of asymptotically convex variational problems
• Remarks on the regularity of the minimizers of certain degenerate functionals
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Boundary regularity for minima of certain quadratic functionals
• On the regularity of the minima of variational integrals
• Regularity for a class of nonlinear elliptic systems
• Regularity for minimizers of non-quadratic functionals: The case \(1<p<2\)
• Elliptic partial differential equations of second order
• A variational approach to doubly nonlinear equations
• Higher integrability for minimizers of integral functionals with \((p,q)\) growth
• Growth conditions and regularity for weak solutions to nonlinear elliptic pdes
• Partial and full boundary regularity for non-autonomous functionals with \(\phi\)-growth conditions
• Gradient bounds for \(p\)-harmonic systems with vanishing Neumann (Dirichlet) data in a convex domain
• Global boundedness of the gradient for a class of nonlinear elliptic systems
• Regularity for some scalar variational problems under general growth conditions
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• The existence of regular boundary points for non-linear elliptic systems
• Regularity theorems for degenerate quasiconvex energies with (p, q)-growth
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations
• Boundary regularity for solutions of degenerate elliptic equations
• Regularity of differential forms minimizing degenerate elliptic functionals.
• Weakly Differentiable Functions
• Lipschitz regularity of solutions of some asymptotically convex problems
• Regularity of minimizers of autonomous convex variational integrals
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• Boundary regularity for manifold constrained p(x)‐harmonic maps
• Real Analysis

This page was built for publication: Boundary regularity for elliptic systems with \(p,q\)-growth