00916nas a2200109   4500008004300000245006700043210006600110260000900176520056500185100002000750856003600770       2000                        en_Ud  00aMinimization of functionals of the gradient by Baire's theorem0 aMinimization of functionals of the gradient by Baires theorem  bSIAM3 a<p>We give sufficient conditions for the existence of solutions of the minimum problem $$ {\mathcal{P}}_{u_0}: \qquad \hbox{Minimize}\quad \int_\Omega g(Du(x))dx, \quad u\in u_0 + W_0^{1,p}(\Omega,{\mathbb{R}}), $$ based on the structure of the epigraph of the lower convex envelope of g, which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space. No convexity conditions are required on g, and no assumptions are made on the boundary datum $u_0\in W_0^{1,p}(\Omega,\mathbb{R})$.</p>1 aZagatti, Sandro  uhttp://hdl.handle.net/1963/3511