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...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15340392_v15_n6_p1975_PerezLlanos |
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| Sumario: | 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. |
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