6533b85cfe1ef96bd12bcba6
RESEARCH PRODUCT
Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data
Sergio Segura De LeónAndrea Dall'agliosubject
Dirichlet problemElliptic partial differential equations; boundary-value problems; regularity; Hölder-continuityregularityOperator (physics)boundary-value problemsElliptic partial differential equationsHölder-continuityMeasure (mathematics)OmegaCombinatoricsBounded functionRadon measurep-LaplacianNabla symbolMathematicsdescription
We prove boundedness and continuity for solutions to the Dirichlet problem for the equation $$ - {\rm{div}}(a(x,\nabla u)) = h(x,u) + \mu ,\;\;\;\;\;{\rm{in}}\;{\rm{\Omega }} \subset \mathbb{R}^{N},$$ where the left-hand side is a Leray-Lions operator from $$- {W}^{1,p}_0(\Omega)$$ into W−1,p′(Ω) with 1 < p < N, h(x,s) is a Caratheodory function which grows like ∣s∣p−1 and μ is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Holder-continuous far from the support of μ.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-08-06 |