Weak Limits in Nonlinear Conductivity
Pablo Pedregal · SIAM Journal on Mathematical Analysis · 2015
The problem of characterizing weak limits of sequences of solutions for a nonlinear diffusion equation of $p$-Laplacian type is addressed. It is formulated in terms of certain moments of underlying Young measures associated with main fields corresponding to the nonlinear equation. We show two main results. One is a necessary condition for a pair of vectors to be such a weak limit; the other one, a sufficient counterpart. Unlike the linear case, those two conditions do not match.