Summability and existence results for quasilinear parabolic equations with Hardy potential term
type: Item
instance of: scholarly article
title: Summability and existence results for quasilinear parabolic equations with Hardy potential term
zbMATH Open document ID: 1262.35131
author: Maria Michaela Porzio
author: Ana Primo
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2013-02-21T00:00:00Z
review text: The authors study the equation \[ u_t = \text{div} (a(x,t,u, \nabla u)) = \lambda \frac{u}{|x|^2} + f, \] where \(a\) is a Caratheodory function and \(f\) is in \(L^r(L^q)\) with \(r,q \geq 1\). The authors prove the existence and the summability of the solutions. Moreover they analyze in detail how the presence of this singular potential and the summability of the datum \(f\) influence the regularity of the solutions.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K67
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6138206
zbMATH Keywords: nonlinear parabolic equations
zbMATH Keywords: Hardy potentials
zbMATH Keywords: regularity of solutions
zbMATH Keywords: singular potential
MaRDI profile type: Publication
full work available at URL: s00030-012-0154-5
OpenAlex ID: W1963774040
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DOI: 10.1007/S00030-012-0154-5
description: scientific article; zbMATH DE number 6138206