Hardy-Sobolev inequalities with singularities on non smooth boundary. Part 2: Influence of the global geometry in small dimensions
نویسندگان
چکیده
We consider Hardy-Sobolev nonlinear equations on domains with singularities. introduced this problem in Cheikh-Ali [4]. Under a local geometric hypothesis, namely that the generalized mean curvature is negative (see (7) below), we proved existence of extremals for relevant inequality large dimensions. In present paper, tackle question small dimensions was left open. introduce “mass”, global quantity, positivity which ensures As byproduct, prove solutions to perturbation initial equation via Mountain-Pass Lemma.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2021
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2020.07.043