scholarly journals Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data

2017 ◽  
Vol 30 (1) ◽  
pp. 31-46
Author(s):  
Hassib Moulay Cherif
Keyword(s):  
Elliptic Equation ◽  
Measure Data ◽  
Strongly Nonlinear ◽  
Regularity Of Solution

scholarly journals Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

2018 ◽  
Vol 36 (2) ◽  
pp. 33-55 ◽  
Author(s):  
Taghi Ahmedatt ◽  
Elhoussine Azroul ◽  
Hassane Hjiaj ◽  
Abdelfattah Touzani
Keyword(s):  
Elliptic Equation ◽  
Variable Exponent ◽  
Nonlinear Term ◽  
Entropy Solutions ◽  
Measure Data ◽  
Nonlinear Elliptic Problems ◽  
Strongly Nonlinear ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic ◽  
Nonstandard Growth Condition

In this paper, we study the existence of entropy solutions for some nonlinear $p(x)-$elliptic equation of the type $$Au - \mbox{div }\phi(u) + H(x,u,\nabla u) = \mu,$$ where $A$ is an operator of Leray-Lions type acting from $W_{0}^{1,p(x)}(\Omega)$ into its dual, the strongly nonlinear term $H$ is assumed only to satisfy some nonstandard growth condition with respect to $|\nabla u|,$ here $\>\phi(\cdot)\in C^{0}(I\!\!R,I\!\!R^{N})\>$ and $\mu$ belongs to ${\mathcal{M}}_{0}^{b}(\Omega)$.

On Existence of L∞-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term

2007 ◽  
Vol 7 (3) ◽  
Author(s):  
J.V. Goncalves ◽  
A.L. Melo ◽  
C.A. Santos
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Term ◽  
Ground States ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Singular Elliptic Equations

AbstractWe establish new results concerning existence and the behavior at infinity of solutions for the singular nonlinear elliptic equation −Δu = ρa(x)u

Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data

2016 ◽  
Vol 23 (3) ◽  
pp. 303-321 ◽  
Author(s):  
Youssef Akdim ◽  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Hicham Redwane
Keyword(s):  
Growth Condition ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Measure Data ◽  
Renormalized Solution ◽  
Unbounded Function ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
The Right

AbstractWe study the existence result of a renormalized solution for a class of nonlinear parabolic equations of the form${\partial b(x,u)\over\partial t}-\operatorname{div}(a(x,t,u,\nabla u))+g(x,t,u% ,\nabla u)+H(x,t,\nabla u)=\mu\quad\text{in }\Omega\times(0,T),$where the right-hand side belongs to ${L^{1}(Q_{T})+L^{p^{\prime}}(0,T;W^{-1,p^{\prime}}(\Omega))}$ and ${b(x,u)}$ is unbounded function of u, ${{-}\operatorname{div}(a(x,t,u,\nabla u))}$ is a Leray–Lions type operator with growth ${|\nabla u|^{p-1}}$ in ${\nabla u}$. The critical growth condition on g is with respect to ${\nabla u}$ and there is no growth condition with respect to u, while the function ${H(x,t,\nabla u)}$ grows as ${|\nabla u|^{p-1}}$.

scholarly journals A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data

2003 ◽  
Vol 41 (6) ◽  
pp. 1997-2031 ◽  
Author(s):  
Jérôme Droniou ◽  
Thierry Gallouët ◽  
Raphaèle Herbin
Keyword(s):  
Elliptic Equation ◽  
Finite Volume ◽  
Measure Data ◽  
Finite Volume Scheme ◽  
Volume Scheme
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