On the convergence of functions from a Sobolev space satisfying special integral estimates

Abstract

UDC 517.9 For sequences of functions from a Sobolev space satisfying special integral estimates, we , in one case, establish a lemma on the choice of pointwise convergent subsequences and, in a different case, prove a theorem on convergence of the corresponding sequences of generalized derivatives in measure. These results are applied to the problem of existence of the entropy solutions of nonlinear equations with degenerate coercivity and L 1 -data.