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A priori estimates for a class of nonuniformly elliptic equations. (English) Zbl 0911.35025

Summary: We prove a priori estimates for solutions of the homogeneous Dirichlet problem for an equation in the form \(-(a_{ij}(x,u)u_{x_j})_{x_i}=f\), where \(\{a_{ij}(x,\eta)\}\) is a matrix of bounded Carathéodory functions which satisfy the inequality \(a_{ij}(x,\eta)\xi_j\xi_i\geq b(|\eta|)|\xi|^2\), where \(b(t)\) is a positive bounded continuous function.

MSC:

35B45 A priori estimates in context of PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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