An entwinement of algebraic topological and variational method to study the {\it Prandtl Batchelor} problem

arXiv2003.04239MaRDI QIDQ6504948

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Abstract: In this paper we study the existence of nontrivial weak solution to a {it Prandtl-Batchelor} type free boundary value elliptic problem involving a $p$-Laplacian operator and a power nonlinearity. Topics from algebraic topology will be used to establish the existence of a solution to the approximating problem, whereas, the variational technique will be used to fix the claim of existence of a solution to the main problem. In the process, a couple of classical results were also improved to suit the purpose of establishing the existence of a nontrivial solution.

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