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 $u_0\in W_0^{1,p}(\Omega,\mathbb{R})$.

%B SIAM J. Control Optim. 38 (2000) 384-399 %I SIAM %G en_US %U http://hdl.handle.net/1963/3511 %1 753 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-12T14:43:10Z\\nNo. of bitstreams: 1\\nzagatti.pdf: 370380 bytes, checksum: 2aed80738302a8c307ad9a1193494f62 (MD5) %R 10.1137/S0363012998335206