We study Harnack inequality and a priori Hölder estimates for weak solutions to a new class of equations (Formula presented.) satisfying the non-uniform ellipticity condition (Formula presented.) where ζ=(ξ,η)∈Rn×Rm,ζ≠0 where A=aij(z)i,j=1,..N is a positive matrix defined on a bounded domain Ω∈RN of points z=(x,t),x∈Rn,t∈Rm,N=n+m;n,m≥1. The weight ω(x,t) is a positive function satisfying also some additional conditions. We prove our results by using Sobolev and Poincare-type inequalities modeled on the non-uniformity of the gradient.
On Harnack inequality and Hölder continuity for non uniformly elliptic equations
Giuseppe Di Fazio
Primo
Membro del Collaboration Group
;
2024-01-01
Abstract
We study Harnack inequality and a priori Hölder estimates for weak solutions to a new class of equations (Formula presented.) satisfying the non-uniform ellipticity condition (Formula presented.) where ζ=(ξ,η)∈Rn×Rm,ζ≠0 where A=aij(z)i,j=1,..N is a positive matrix defined on a bounded domain Ω∈RN of points z=(x,t),x∈Rn,t∈Rm,N=n+m;n,m≥1. The weight ω(x,t) is a positive function satisfying also some additional conditions. We prove our results by using Sobolev and Poincare-type inequalities modeled on the non-uniformity of the gradient.File in questo prodotto:
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