higher integrability of the gradient in degenerate elliptic equations

Pierre Dreyfuss (1)

1 IECN - Institut Élie Cartan de Nancy

We prove that under some global conditions on the maximum and the minimum eigenvalue of the matrix of the coefficients, the gradient of the (weak) solution of some degenerate elliptic equations has higher integrability than expected. Technically we adapt the Giaquinta-Modica regularity method in some degenerate cases. When the dimension is two, a consequence of our result is a new Holder continuity result for the weak solution

Mots clés: degenerate elliptic equations; regularity of solutions; weigths

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Dreyfuss. higher integrability of the gradient in degenerate elliptic equations. Potential Analysis, 2007, 26, pp.101-119. ⟨10.1007/s11118-006-9030-4⟩. ⟨hal-00095063⟩