Regularity under general and \(p,q\)-growth conditions

DOI10.3934/dcdss.2020155zbMath1439.35102OpenAlexW2988728610MaRDI QIDQ2182837

Paolo Marcellini

Publication date: 26 May 2020

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2020155

zbMATH Keywords

regularity of solutionslocal Lipschitz continuitygeneral growth conditionselliptic equations and systemsparabolic equations and systems

Mathematics Subject Classification ID

Variational inequalities (49J40) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60) A priori estimates in context of PDEs (35B45) Second-order parabolic systems (35K40) Second-order elliptic systems (35J47)

Related Items (38)

Local boundedness for solutions of a class of nonlinear elliptic systems ⋮ The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth ⋮ Regularity results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions ⋮ Borderline Lipschitz regularity for bounded minimizers of functionals with \((p,q)\)-growth ⋮ Regularity for obstacle problems without structure conditions ⋮ On the local behavior of local weak solutions to some singular anisotropic elliptic equations ⋮ Weak differentiability to nonuniform nonlinear degenerate elliptic systems under \(p\), \(q\)-growth condition on the Heisenberg group ⋮ The nonlinear \((p,q)\)-Schrödinger equation with a general nonlinearity: existence and concentration ⋮ Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion ⋮ Unnamed Item ⋮ Parabolic Harnack estimates for anisotropic slow diffusion ⋮ Multiple solutions for double phase problems in \(\mathbb{R}^n\) via Ricceri's principle ⋮ Regularity results for bounded solutions to obstacle problems with non-standard growth conditions ⋮ Local boundedness of variational solutions to nonlocal double phase parabolic equations ⋮ The Sobolev class where a weak solution is a local minimizer ⋮ An extension of De Giorgi class and applications ⋮ Bloch estimates in non-doubling generalized Orlicz spaces ⋮ Local boundedness of weak solutions to elliptic equations with \(p, q\)-growth ⋮ Lipschitz regularity for degenerate elliptic integrals with \(p, q\)-growth ⋮ Fractional double-phase patterns: concentration and multiplicity of solutions ⋮ Boundedness of the solutions of a kind of nonlinear parabolic systems ⋮ Lipschitz regularity results for a class of obstacle problems with nearly linear growth ⋮ Interpolative gap bounds for nonautonomous integrals ⋮ Existence and multiplicity results for double phase problem with nonlinear boundary condition ⋮ Growth conditions and regularity for weak solutions to nonlinear elliptic pdes ⋮ Unnamed Item ⋮ Higher differentiability for a class of obstacle problems with nearly linear growth conditions ⋮ Interpolative gap bounds for nonautonomous integrals ⋮ On the regularity of solutions to a class of degenerate PDE's with lower order terms ⋮ Minimizers of convex functionals with small degeneracy set ⋮ Developments and perspectives in nonlinear potential theory ⋮ \( W^{2, p} \)-regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values ⋮ Unnamed Item ⋮ A-priori gradient bound for elliptic systems under either slow or fast growth conditions ⋮ Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements ⋮ On Hölder continuity and equivalent formulation of intrinsic Harnack estimates for an anisotropic parabolic degenerate prototype equation ⋮ Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence ⋮ Existence of variational solutions to nonlocal evolution equations via convex minimization

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