Some remarks on the regularity of weak solutions of degenerate elliptic systems. (English) Zbl 0902.35021

Esposito, Luca; Mingione, Giuseppe

Rev. Mat. Complut. 11, No. 1, 203-219 (1998).

The authors prove the existence of second order derivatives of the weak solutions \(u \in W^{1,p}\) of the system \(\text{ div} A(\nabla u) = 0\) with degeneracy assumptions on \(A(x).\) Monotonicity about the vector field \(A(x)\) is assumed.

Reviewer: G.Di Fazio (Catania)

MSC:

35B65	Smoothness and regularity of solutions to PDEs
35J60	Nonlinear elliptic equations
35J70	Degenerate elliptic equations

Keywords:

existence of second order derivatives