Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities
In this paper we analyze the following elliptic problem related to some Caffarelli-Kohn-Nirenberg inequalities: where is a domain such that 0 and c; p are positive constants verifying 0 < and p > Our study concerns to existence of solutions to the former problem. More precisely, first we deter...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15340392_v15_n6_p1975_PerezLlanos |
| Aporte de: |
| id |
todo:paper_15340392_v15_n6_p1975_PerezLlanos |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_15340392_v15_n6_p1975_PerezLlanos2023-10-03T16:21:36Z Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities Perez-Llanos, M. Caffarelli-Kohn-Nirenberg inequality Hardy potential Weighted Sobolev Spaces In this paper we analyze the following elliptic problem related to some Caffarelli-Kohn-Nirenberg inequalities: where is a domain such that 0 and c; p are positive constants verifying 0 < and p > Our study concerns to existence of solutions to the former problem. More precisely, first we determine a critical thereshold for the power p, in the sense that, beyond this value it does not exist any positive supersolution to our problem, not even in a very weak sense. In addition, we show existence of solutions for all the values 0 below this threshold, with the restriction whenever the righthand side verifies if When it suffices that The existence of solutions for is an open question. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15340392_v15_n6_p1975_PerezLlanos |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Caffarelli-Kohn-Nirenberg inequality Hardy potential Weighted Sobolev Spaces |
| spellingShingle |
Caffarelli-Kohn-Nirenberg inequality Hardy potential Weighted Sobolev Spaces Perez-Llanos, M. Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| topic_facet |
Caffarelli-Kohn-Nirenberg inequality Hardy potential Weighted Sobolev Spaces |
| description |
In this paper we analyze the following elliptic problem related to some Caffarelli-Kohn-Nirenberg inequalities: where is a domain such that 0 and c; p are positive constants verifying 0 < and p > Our study concerns to existence of solutions to the former problem. More precisely, first we determine a critical thereshold for the power p, in the sense that, beyond this value it does not exist any positive supersolution to our problem, not even in a very weak sense. In addition, we show existence of solutions for all the values 0 below this threshold, with the restriction whenever the righthand side verifies if When it suffices that The existence of solutions for is an open question. |
| format |
JOUR |
| author |
Perez-Llanos, M. |
| author_facet |
Perez-Llanos, M. |
| author_sort |
Perez-Llanos, M. |
| title |
Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| title_short |
Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| title_full |
Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| title_fullStr |
Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| title_full_unstemmed |
Optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| title_sort |
optimal power for an elliptic equation related to some caffarelli-kohn-nirenberg inequalities |
| url |
http://hdl.handle.net/20.500.12110/paper_15340392_v15_n6_p1975_PerezLlanos |
| work_keys_str_mv |
AT perezllanosm optimalpowerforanellipticequationrelatedtosomecaffarellikohnnirenberginequalities |
| _version_ |
1807320014213087232 |