Local Lipschitz continuity for \(p, q\)-PDEs with explicit \(u\)-dependence

DOI10.1016/j.na.2022.113066zbMath1501.35188OpenAlexW4288906206WikidataQ114145996 ScholiaQ114145996MaRDI QIDQ2094276

Paolo Marcellini

Publication date: 28 October 2022

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

Full work available at URL: https://doi.org/10.1016/j.na.2022.113066

zbMATH Keywords

calculus of variationsregularity of solutionsnonlinear elliptic equations in divergence form

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60)

Related Items (12)

Divergent sequence of nontrivial solutions for superlinear double phase problems ⋮ Parametric anisotropic singular equations with \([p(z), q(z)\)-growth conditions and indefinite perturbation] ⋮ Lipschitz regularity of minimizers of variational integrals with variable exponents ⋮ A new kind of double phase elliptic inclusions with logarithmic perturbation terms. II: Applications ⋮ The Sobolev class where a weak solution is a local minimizer ⋮ Existence of ground state solutions for a Choquard double phase problem ⋮ Non‐autonomous double phase eigenvalue problems with indefinite weight and lack of compactness ⋮ Local boundedness of weak solutions to elliptic equations with \(p, q\)-growth ⋮ Regularizing effect in some Mingione's double phase problems with very singular data ⋮ Partial regularity for steady double phase fluids ⋮ Nonautonomous double‐phase equations with strong singularity and concave perturbation ⋮ Boundedness of the solutions of a kind of nonlinear parabolic systems

Cites Work

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• Parabolic equations with \(p,q\)-growth
• Parabolic systems with \({p,q}\)-growth: a variational approach
• Local boundedness of minimizers with limit growth conditions
• Higher differentiability for \(n\)-harmonic systems with Sobolev coefficients
• Higher integrability for minimizers of asymptotically convex integrals with discontinuous coefficients
• Regularity of minimizers under limit growth conditions
• Global gradient estimates for non-uniformly elliptic equations
• Higher differentiability of minimizers of convex variational integrals
• Gradient estimates via linear and nonlinear potentials
• Lebesgue and Sobolev spaces with variable exponents
• Local boundedness of solutions to quasilinear elliptic systems
• Degenerate parabolic equations
• Regularity for elliptic equations with general growth conditions
• Local regularity for an anisotropic elliptic equation
• A-priori gradient bound for elliptic systems under either slow or fast growth conditions
• Higher integrability for variational integrals with non-standard growth
• Regularity of relaxed minimizers of quasiconvex variational integrals with \((p, q)\)-growth
• Hölder continuity of solutions to an anisotropic elliptic equation
• Global Lipschitz regularity for almost minimizers of asymptotically convex variational problems
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Regularity for minima of functionals with p-growth
• Regularity for a more general class of quasilinear equations
• On Lavrentiev's phenomenon
• Nonuniformly elliptic energy integrals with \(p, q\)-growth
• A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces
• Remarks on local boundedness and local holder continuity of local weak solutions to anisotropic \(p\)-Laplacian type equations
• Local Lipschitz continuity of minimizers with mild assumptions on the \(x\)-dependence
• Regularity for general functionals with double phase
• Double phase anisotropic variational problems and combined effects of reaction and absorption terms
• Higher differentiability for solutions to a class of obstacle problems
• Higher integrability for minimizers of integral functionals with \((p,q)\) growth
• A new proof of local \(C^{1,\alpha}\) regularity for solutions of certain degenerate elliptic P.D.E
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• New examples on Lavrentiev gap using fractals
• Existence and regularity for elliptic equations under \(p,q\)-growth
• Lavrentiev gap for some classes of generalized Orlicz functions
• Growth conditions and regularity for weak solutions to nonlinear elliptic pdes
• Splitting-type variational problems with mixed linear-superlinear growth conditions
• Recent developments in problems with nonstandard growth and nonuniform ellipticity
• Resonant double phase equations
• Lipschitz bounds and nonautonomous integrals
• Quasiconvexity and partial regularity via nonlinear potentials
• Existence of radial solutions for a \(p(x)\)-Laplacian Dirichlet problem
• Regularity under general and \(p,q\)-growth conditions
• Regularity properties for quasiminimizers of a \((p, q)\)-Dirichlet integral
• Regularity for double phase variational problems
• Removable sets in non-uniformly elliptic problems
• A variational approach to parabolic equations under general and \(p,q\)-growth conditions
• Regularity for minimizers for functionals of double phase with variable exponents
• Existence of evolutionary variational solutions via the calculus of variations
• Global boundedness of the gradient for a class of nonlinear elliptic systems
• Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent
• Regularity of minimizers of \(W^{1,p}\)-quasiconvex variational integrals with \((p,q)\)-growth
• Linear and quasilinear elliptic equations
• The boundedness of generalized solutions of elliptic differential equations
• Regularity for some scalar variational problems under general growth conditions
• An alternative approach to the Hölder continuity of solutions to some elliptic equations
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• On the regularity of minimizers for scalar integral functionals with \((p,q)\)-growth
• Boundary regularity for elliptic systems with \(p,q\)-growth
• Existence and multiplicity of solutions for a class ofp&qelliptic problems with critical exponent
• Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations
• Wang’s multiplicity result for superlinear $(p,q)$–equations without the Ambrosetti–Rabinowitz condition
• Existence of weak solutions for elliptic systems with p,q-growth
• Remarks on strongly elliptic partial differential equations
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Hölder estimates for nonlinear degenerate parabolic sytems.
• Regularity theorems for degenerate quasiconvex energies with (p, q)-growth
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• On the Higher Integrability of the Gradient of Weak Solutions of Certain Degenerate Elliptic Systems
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• Integral Convexity and Parabolic Systems
• Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations
• Lipschitz Bounds and Nonuniform Ellipticity
• Growth conditions and regularity, an optimal local boundedness result
• Higher differentiability of minimizers of variational integrals with Sobolev coefficients

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