\(L^q\)-\(L^\infty\) Hölder continuity for quasilinear parabolic equations associated to Sobolev derivations

DOI10.1016/S0022-247X(02)00084-7zbMath1016.35032OpenAlexW2071427910MaRDI QIDQ697446

Gabriele Grillo, Fabio Cipriano

Publication date: 17 September 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00084-7

zbMATH Keywords

regularitySobolev inequality\(p\)-Laplacian-like operatorabstract nonlinear evolution equationssub-Riemannian \(p\)-Laplacian

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Markov semigroups and applications to diffusion processes (47D07)

Related Items (11)

Local Lipschitz continuity of the inverse of the fractional \(p\)-Laplacian, Hölder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains ⋮ The Cauchy problem for the fast \(p\)-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour ⋮ Quasilinear parabolic equations with nonlinear Wentzell-Robin type boundary conditions ⋮ The \(p\)-Laplace operator with the nonlocal Robin boundary conditions on arbitrary open sets ⋮ Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions ⋮ Fine regularity for elliptic and parabolic anisotropic Robin problems with variable exponents ⋮ Quasi-linear Venttsel' problems with nonlocal boundary conditions on fractal domains ⋮ Nonlinear maximal monotone extensions of symmetric operators ⋮ Hypercontractivity, Nash inequalities and subordination for classes of nonlinear semigroups ⋮ The heat equation with nonlinear generalized Robin boundary conditions ⋮ Asymptotics of the porous media equation via Sobolev inequalities

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