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Volume 35, Issue 2
The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data

Hichem Khelifi

DOI: 10.4208/jpde.v35.n2.1

J. Part. Diff. Eq., 35 (2022), pp. 101-122.

Published online: 2022-04

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  • Abstract

The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity, and $L^{1}-$data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. We prove the existence of an entropy solution and show its continuous dependence on the $L^{1}-$data in $W^{1,q(\cdot)}(\Omega)$ with some $q(\cdot)>1$.

  • Keywords

Ostacle problem, Degenerate Coercivity, Variable exponents, $L^1$ data, Truncation function.

  • AMS Subject Headings

35J70, 35J60, 35B65, 35J87

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

khelifi.hichemedp@gmail.com (Hichem Khelifi)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-35-101, author = {Khelifi , Hichem}, title = {The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {2}, pages = {101--122}, abstract = {

The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity, and $L^{1}-$data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. We prove the existence of an entropy solution and show its continuous dependence on the $L^{1}-$data in $W^{1,q(\cdot)}(\Omega)$ with some $q(\cdot)>1$.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n2.1}, url = {http://global-sci.org/intro/article_detail/jpde/20444.html} }
TY - JOUR T1 - The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data AU - Khelifi , Hichem JO - Journal of Partial Differential Equations VL - 2 SP - 101 EP - 122 PY - 2022 DA - 2022/04 SN - 35 DO - http://doi.org/10.4208/jpde.v35.n2.1 UR - https://global-sci.org/intro/article_detail/jpde/20444.html KW - Ostacle problem, Degenerate Coercivity, Variable exponents, $L^1$ data, Truncation function. AB -

The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity, and $L^{1}-$data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. We prove the existence of an entropy solution and show its continuous dependence on the $L^{1}-$data in $W^{1,q(\cdot)}(\Omega)$ with some $q(\cdot)>1$.

Khelifi , Hichem. (2022). The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data. Journal of Partial Differential Equations. 35 (2). 101-122. doi:10.4208/jpde.v35.n2.1
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