An existence result for superparabolic functions

DOI10.1016/j.jfa.2009.08.009zbMath1184.35185OpenAlexW1971844998WikidataQ110085996 ScholiaQ110085996MaRDI QIDQ1048181

Juha Kinnunen, Teemu Lukkari, Mikko Parviainen

Publication date: 11 January 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.08.009

zbMATH Keywords

measure dataparabolic comparison principle

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Quasilinear parabolic equations with (p)-Laplacian (35K92) Quasilinear parabolic equations (35K59)

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Nonlinear parabolic capacity and polar sets of superparabolic functions ⋮ Regularity of Supersolutions ⋮ Local approximation of superharmonic and superparabolic functions in nonlinear potential theory ⋮ Global weighted Orlicz estimates for parabolic measure data problems: application to estimates in variable exponent spaces ⋮ Characterizations of interior polar sets for the degenerate \(p\)-parabolic equation ⋮ Regularity estimates for singular parabolic measure data problems with sharp growth ⋮ Unbounded supersolutions of some quasilinear parabolic equations: a dichotomy ⋮ The porous medium equation with measure data ⋮ The Wolff gradient bound for degenerate parabolic equations ⋮ Riesz potentials and nonlinear parabolic equations ⋮ Borderline gradient continuity for nonlinear parabolic systems ⋮ Global regularity for degenerate/singular parabolic equations involving measure data ⋮ Irregular time dependent obstacles ⋮ Shadows of infinities ⋮ Variational parabolic capacity

Cites Work

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• A connection between a general class of superparabolic functions and supersolutions
• Lower semicontinuity of weak supersolutions to nonlinear parabolic equations.
• Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation
• Degenerate parabolic equations
• Nonlinear elliptic and parabolic equations involving measure data
• Harnack estimates for quasi-linear degenerate parabolic differential equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Nonlinear parabolic equations with measure data
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• On the Dirichlet Boundary Value Problem for a Degenerate Parabolic Equation