This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we prove an a priori estimate in a weighted space of continuous functions. From this compactness result, the existence of a solution to our problem is proved by exploiting the homotopy invariance of the Leray-Schauder degree.
Felli, V., Schneider, M. (2005). Compactness and existence results for degenerate critical elliptic equations. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 7(1), 37-73 [10.1142/S0219199705001623].
Compactness and existence results for degenerate critical elliptic equations
FELLI, VERONICA;
2005
Abstract
This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we prove an a priori estimate in a weighted space of continuous functions. From this compactness result, the existence of a solution to our problem is proved by exploiting the homotopy invariance of the Leray-Schauder degree.
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