Existence and regularity of positive solutions of a degenerate fourth order elliptic problem
KeywordsEmbedding theorem, fourth order operator equations, degenerate elliptic problem
AbstractIn this paper, we consider existence and regularity of positive solutions of a degenerate fourth order elliptic problem. Firstly, a new Caffarelli-Kohn-Nirenberg type inequality for the fourth order case is established. Then, by the use of the corresponding embedding, we obtain the existence of positive solutions of a degenerate fourth order elliptic problem. Finally, the regularity of the positive solutions is also studied.
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