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On a class of degenerate elliptic equations in weighted Hölder spaces. (English) Zbl 1150.35420

The paper is devoted to the study of the Dirichlet problem for the degenerate elliptic equation \[ P_0\Delta u+\gamma (\nabla P_0,\nabla u)=f(x,u,\nabla u) \text{ in } \Omega ,\quad u=0 \text{ on } \partial \Omega , \] where \(\gamma \geq 0\) is a given parameter, \(\Omega \subset \mathbb R^n\) is an annular region, the given function \(P_0(x)\) is such that \(| \nabla P_0| +P_0\geq \varepsilon >0\) in \(\overline \Omega \), and \(P_0=0\) on the outer boundary of \(\Omega \). The existence of a unique classical solution is proved via Schauder estimates in Hölder spaces.

MSC:

35J70 Degenerate elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B65 Smoothness and regularity of solutions to PDEs
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