COMPACTNESS AND EXISTENCE RESULTS FOR DEGENERATE CRITICAL ELLIPTIC EQUATIONS
Veronica Felli, Matthias Schneider · Communications in Contemporary Mathematics · 2005
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.