Boccardo, Lucio The summability of solutions to variational problems since Guido Stampacchia. (English) Zbl 1129.35371 RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 97, No. 3, 413-421 (2003). Summary: Inequalities concerning the integral of \(|\nabla u|^2\) on the subsets where \(|u(x)|\) is greater than \(k\) can be used in order to prove regularity properties of the function \(u\). This method was introduced by Ennio De Giorgi e Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. Cited in 4 Documents MSC: 35J60 Nonlinear elliptic equations 35B45 A priori estimates in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs 35D10 Regularity of generalized solutions of PDE (MSC2000) 35J20 Variational methods for second-order elliptic equations 49N60 Regularity of solutions in optimal control PDFBibTeX XMLCite \textit{L. Boccardo}, RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 97, No. 3, 413--421 (2003; Zbl 1129.35371) Full Text: EuDML