Une métrique associée à une classe d’opérateurs elliptiques dégénérés. (French) Zbl 0553.35033

Franchi, Bruno; Lanconelli, Ermanno

Rend. Sem. Mat., Torino, Fasc. Spec., Linear partial and pseudo-differential operators, Conv. Torino/Italy 1982, 105-114 (1983).

[For the entire collection see Zbl 0533.00013.]
The authors prove the local Hölder continuity of weak solutions of certain classes of degenerate elliptic equations \(L=\sum^{n}_{i,j=1}(\partial /\partial x_ j)(a_{ij}\partial /\partial x_ i)\) where \(a_{ij}\in L^{\infty}(R^ n)\) is a symmetric, nonnegative matrix defined in \(R^ n\). Under certain conditions and the existence of functions \(\lambda_ 1,...,\lambda_ n\) they can use the same methods as Bombieri-Moser to obtain the classical Hölder inequality for weak solutions of \(Lu=0\) in \(\Omega\) if \(\Omega\) is a locally \((\lambda_ 1,...,\lambda_ n)\) convex open subset of \(R^ n\).

Reviewer: V.Massari

MSC:

35J70	Degenerate elliptic equations
35D10	Regularity of generalized solutions of PDE (MSC2000)
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

local Hölder continuity; weak solutions

Citations:

Zbl 0533.00013