Regularity and time behavior of the solutions to weak monotone parabolic equations

DOI10.1007/s00028-021-00709-yzbMath1481.35260OpenAlexW3160521068MaRDI QIDQ2064539

Maria Michaela Porzio

Publication date: 6 January 2022

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-021-00709-y

zbMATH Keywords

decay estimatesimmediate regularization

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quasilinear parabolic equations (35K59)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some borderline cases of nonlinear parabolic equations with irregular data
• Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities
• On decay estimates
• On uniform and decay estimates for unbounded solutions of partial differential equations
• Quantitative asymptotic estimates for evolution problems
• Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems
• Approximated solutions of equations with \(L^ 1\) data. Application to the \(H\)-convergence of quasilinear parabolic equations
• Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations
• Degenerate parabolic equations
• Doubly nonlinear equations of porous medium type
• Non-negative solutions of the evolution p-Laplacian equation. Initial traces and Cauchy problem when \(1<p<2\)
• Super and ultracontractive bounds for doubly nonlinear evolution equations
• Nonlinear elliptic and parabolic equations involving measure data
• Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation
• Summability and existence results for nonlinear parabolic equations
• Singular evolution on manifolds, their smoothing properties, and Sobolev inequalities
• Pointwise decay for the solutions of degenerate and singular parabolic equations
• Existence results for some nonlinear parabolic equations with nonregular data
• Nonlinear parabolic equations with measure data
• Ultracontractivity and convergence to equilibrium for supercritical quasilinear parabolic equations on Riemannian manifolds
• Existence of solutions for some ``noncoercive parabolic equations
• A new approach to decay estimates - application to a nonlinear and degenerate parabolic PDE
• Regularity and time behavior of the solutions of linear and quasilinear parabolic equations
• Asymptotic behavior and regularity properties of strongly nonlinear parabolic equations
• Parabolic equations with nonlinear, degenerate and space-time dependent operators
• \(L^r_{\mathrm{loc}}-L^\infty_{\mathrm{loc}}\) estimates and expansion of positivity for a class of doubly non linear singular parabolic equations
• Riesz potentials and nonlinear parabolic equations
• Local behavior of solutions of quasilinear parabolic equations
• On the Cauchy Problem and Initial Traces for a Degenerate Parabolic Equation
• Existence and uniqueness of “entropy” solutions of parabolic problems with L1 data
• Continuity of Solutions of Parabolic and Elliptic Equations
• Problems paraboliques semi-lineaires avec donnees measures
• Effets régularisants de semi-groupes non linéaires dans des espaces de Banach
• Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem
• Lloc∞-estimates for degenerate and singular parabolic equations
• Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data
• The smoothing property for a class of doubly nonlinear parabolic equations
• The Cauchy problem for ut = div(|▿u|p−2▿u) when
• On the Existence of Solutions of the Cauchy Problem for a Doubly Nonlinear Parabolic Equation
• Correetion to “A Harnack Inequality for Parabolic Differential Equations”
• Higher integrability for doubly nonlinear parabolic systems
• Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems
• Uniform bounds for solutions to quasilinear parabolic equations.