Existence of weak solutions for elliptic Dirichlet problems with variable exponent

Sungchol Kim; Dukman Ri

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 3, page 283-302
  • ISSN: 0862-7959

Abstract

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This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type - div a ( x , u , ∇ u ) + b ( x , u , ∇ u ) = 0 in Ω , u = 0 on ∂ Ω , where Ω is a bounded domain of ℝ n , n ≥ 2 . In particular, we do not require strict monotonicity of the principal part a ( x , z , · ) , while the approach is based on the variational method and results of the variable exponent function spaces.

How to cite

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Kim, Sungchol, and Ri, Dukman. "Existence of weak solutions for elliptic Dirichlet problems with variable exponent." Mathematica Bohemica 148.3 (2023): 283-302. <http://eudml.org/doc/299098>.

@article{Kim2023,
abstract = {This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type \[ \{\left\lbrace \begin\{array\}\{ll\} -\{\rm div\} a(x, u, \nabla u)+b(x, u, \nabla u)=0 &\text\{in\} \ \Omega ,\\ u=0 &\text\{on\} \ \partial \Omega , \end\{array\}\right.\} \] where $\Omega $ is a bounded domain of $\mathbb \{R\}^n$, $n\ge 2$. In particular, we do not require strict monotonicity of the principal part $a(x,z,\cdot )$, while the approach is based on the variational method and results of the variable exponent function spaces.},
author = {Kim, Sungchol, Ri, Dukman},
journal = {Mathematica Bohemica},
keywords = {variable exponent; existence; variational methods; Dirichlet problem},
language = {eng},
number = {3},
pages = {283-302},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of weak solutions for elliptic Dirichlet problems with variable exponent},
url = {http://eudml.org/doc/299098},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Kim, Sungchol
AU - Ri, Dukman
TI - Existence of weak solutions for elliptic Dirichlet problems with variable exponent
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 3
SP - 283
EP - 302
AB - This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type \[ {\left\lbrace \begin{array}{ll} -{\rm div} a(x, u, \nabla u)+b(x, u, \nabla u)=0 &\text{in} \ \Omega ,\\ u=0 &\text{on} \ \partial \Omega , \end{array}\right.} \] where $\Omega $ is a bounded domain of $\mathbb {R}^n$, $n\ge 2$. In particular, we do not require strict monotonicity of the principal part $a(x,z,\cdot )$, while the approach is based on the variational method and results of the variable exponent function spaces.
LA - eng
KW - variable exponent; existence; variational methods; Dirichlet problem
UR - http://eudml.org/doc/299098
ER -

References

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