Arcoya, David; Boccardo, Lucio Some remarks on critical point theory for nondifferentiable functionals. (English) Zbl 0923.35049 NoDEA, Nonlinear Differ. Equ. Appl. 6, No. 1, 79-100 (1999). The authors study the existence of critical points of nondifferentiable functionals \(J\) of the kind \[ J(v)= \int_\Omega A(x,v)|\nabla v|^2- F(x,v) \] with \(A(x,v)\) a Carathéodory function bounded between positive constant and with bounded derivative respect to the variable \(z\), and \(F(x,z)\) is the primitive of a (Carathéodory) nonlinearity \(f(x,z)\) satisfying suitable hypotheses. Since \(J\) is just differentiable along bounded directions, a suitable compactness condition is introduced. Reviewer: S.Balint (Timişoara) Cited in 30 Documents MSC: 35J20 Variational methods for second-order elliptic equations 49J52 Nonsmooth analysis Keywords:existence; compactness condition PDFBibTeX XMLCite \textit{D. Arcoya} and \textit{L. Boccardo}, NoDEA, Nonlinear Differ. Equ. Appl. 6, No. 1, 79--100 (1999; Zbl 0923.35049) Full Text: DOI