Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces
In this article, we consider three types of solutions in Orlicz spaces for the quasilinear elliptic problem $$ -\hbox{div}(a(|\nabla u|)\nabla u)=0. $$ By applying a comparison principle, we establish the relationships between viscosity supersolutions, weak supersolutions, and superharmonic f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/265/abstr.html |
| _version_ | 1811234816435159040 |
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| author | Fei Fang Zheng Zhou |
| author_facet | Fei Fang Zheng Zhou |
| author_sort | Fei Fang |
| collection | DOAJ |
| description | In this article, we consider three types of
solutions in Orlicz spaces for the quasilinear elliptic problem
$$
-\hbox{div}(a(|\nabla u|)\nabla u)=0.
$$
By applying a comparison principle, we establish the relationships between
viscosity supersolutions, weak supersolutions, and superharmonic functions. |
| first_indexed | 2024-04-12T11:41:48Z |
| format | Article |
| id | doaj.art-457dde04087e497b9544e99297ee6828 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T11:41:48Z |
| publishDate | 2014-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-457dde04087e497b9544e99297ee68282022-12-22T03:34:34ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-12-012014265,110Relationship between solutions to a quasilinear elliptic equation in Orlicz spacesFei Fang0Zheng Zhou1 Peking Univ., Beijing, China Xiamen Univ. of Technology, Xiamen, China In this article, we consider three types of solutions in Orlicz spaces for the quasilinear elliptic problem $$ -\hbox{div}(a(|\nabla u|)\nabla u)=0. $$ By applying a comparison principle, we establish the relationships between viscosity supersolutions, weak supersolutions, and superharmonic functions.http://ejde.math.txstate.edu/Volumes/2014/265/abstr.htmlOilicz-Sobolev spacesquasilinear elliptic equationviscous solution |
| spellingShingle | Fei Fang Zheng Zhou Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces Electronic Journal of Differential Equations Oilicz-Sobolev spaces quasilinear elliptic equation viscous solution |
| title | Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces |
| title_full | Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces |
| title_fullStr | Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces |
| title_full_unstemmed | Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces |
| title_short | Relationship between solutions to a quasilinear elliptic equation in Orlicz spaces |
| title_sort | relationship between solutions to a quasilinear elliptic equation in orlicz spaces |
| topic | Oilicz-Sobolev spaces quasilinear elliptic equation viscous solution |
| url | http://ejde.math.txstate.edu/Volumes/2014/265/abstr.html |
| work_keys_str_mv | AT feifang relationshipbetweensolutionstoaquasilinearellipticequationinorliczspaces AT zhengzhou relationshipbetweensolutionstoaquasilinearellipticequationinorliczspaces |