Mixed boundary value problem for a class of quasi-linear elliptic operators containing $p$-Laplacian

Authors: JUNICHI ARAMAKI

Abstract: In this paper, we consider a mixed boundary value problem to a class of quasi-linear elliptic operators containing a $p$-Laplace operator. We show the existence of a unique weak solution and an estimate. We also demonstrate the continuity of the solution on the given data. Moreover, we consider the dual problem.

Keywords: Mixed boundary value problem, $p$-Laplacian, existence of a weak solution, variational method, continuous dependence of solution, dual problem

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