Alvino, Angelo; Ferone, Vincenzo; Trombetti, Guido A priori estimates for a class of nonuniformly elliptic equations. (English) Zbl 0911.35025 Atti Semin. Mat. Fis. Univ. Modena 46, Suppl., 381-391 (1998). 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. Cited in 28 Documents MSC: 35B45 A priori estimates in context of PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations PDFBibTeX XMLCite \textit{A. Alvino} et al., Atti Semin. Mat. Fis. Univ. Modena 46, 381--391 (1998; Zbl 0911.35025)