A-priori gradient bound for elliptic systems under either slow or fast growth conditions

DOI10.1007/s00526-020-01769-7zbMath1442.35049arXiv1910.04158OpenAlexW3037937930MaRDI QIDQ776038

Paolo Marcellini, Tommaso Di Marco

Publication date: 30 June 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.04158

zbMATH Keywords

calculus of variationslocal Lipschitz continuitygeneral growth conditions\(p,q\)-growth conditions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Methods involving semicontinuity and convergence; relaxation (49J45) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62) Boundary value problems for second-order elliptic systems (35J57)

Related Items (14)

Local Lipschitz continuity for energy integrals with slow growth ⋮ A pointwise differential inequality and second-order regularity for nonlinear elliptic systems ⋮ Generalized superharmonic functions with strongly nonlinear operator ⋮ Unnamed Item ⋮ Wolff potentials and measure data vectorial problems with Orlicz growth ⋮ Local boundedness of weak solutions to elliptic equations with \(p, q\)-growth ⋮ Lipschitz regularity for degenerate elliptic integrals with \(p, q\)-growth ⋮ Very degenerate elliptic equations under almost critical Sobolev regularity ⋮ Gradient bounds for solutions to irregular parabolic equations with \((p, q)\)-growth ⋮ Growth conditions and regularity for weak solutions to nonlinear elliptic pdes ⋮ Recent developments in problems with nonstandard growth and nonuniform ellipticity ⋮ Lipschitz bounds and nonautonomous integrals ⋮ Unnamed Item ⋮ Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence

Cites Work

• Unnamed Item
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• Lipschitz continuity for energy integrals with variable exponents
• Some singular minimizers in low dimensions in the calculus of variations
• Lipschitz estimates for systems with ellipticity conditions at infinity
• Parabolic equations with \(p,q\)-growth
• Nonlocal diffusion equations
• Bounded minimisers of double phase variational integrals
• Hölder regularity of quasiminimizers under generalized growth conditions
• Local boundedness of solutions to quasilinear elliptic systems
• Regularity for scalar integrals without structure conditions
• Nonlinear elliptic systems with general growth
• Minimizers of convex functionals arising in random surfaces
• Regularity under sharp anisotropic general growth conditions
• Regularity for a class of nonlinear elliptic systems
• A singular minimizer of a smooth strongly convex functional in three dimensions
• Pointwise bounds for minimizers of some anisotropic functionals
• Double phase problems with variable growth
• Nonuniformly elliptic energy integrals with \(p, q\)-growth
• A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces
• Regularity results for vectorial minimizers of a class of degenerate convex integrals
• Regularity for general functionals with double phase
• Double phase anisotropic variational problems and combined effects of reaction and absorption terms
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• On the regularity of minima of non-autonomous functionals
• Regularity under general and \(p,q\)-growth conditions
• Regularity for double phase variational problems
• Minimizers of convex functionals with small degeneracy set
• Developments and perspectives in nonlinear potential theory
• A variational approach to parabolic equations under general and \(p,q\)-growth conditions
• Parabolic equation in time and space dependent anisotropic Musielak-Orlicz spaces in absence of Lavrentiev's phenomenon
• Harnack inequalities for double phase functionals
• Higher integrability for constrained minimizers of integral functionals with \((p, q)\)-growth in low dimension
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Non-autonomous functionals, borderline cases and related function classes
• Everywhere regularity for vectorial functionals with general growth
• Integral Convexity and Parabolic Systems
• Lipschitz Bounds and Nonuniform Ellipticity

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