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We investigate the parabolic Boundary Harnack Principle for both divergence and non-divergence type operators by the analytical methods we developed in the elliptic context. Besides the classical case, we deal with less regular space-time domains, including slit domains.
We investigate the Boundary Harnack Principle in Holder domains of exponent $alpha>0$ by the analytical method developed in our previous work A short proof of Boundary Harnack Principle.
We introduce a new boundary Harnack principle in Lipschitz domains for equations with right hand side. Our approach, which uses comparisons and blow-ups, will adapt to more general domains as well as other types of operators. We prove the principle f
We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and $p$-Laplace type equations with a right hand side, as well as for the Laplace equation on nontangentially accessible domains under extra conditions
We consider second-order linear parabolic operators in non-divergence form that are intrinsically defined on Riemannian manifolds. In the elliptic case, Cabre proved a global Krylov-Safonov Harnack inequality under the assumption that the sectional c
In this note we consider problems related to parabolic partial differential equations in geodesic metric measure spaces, that are equipped with a doubling measure and a Poincare inequality. We prove a location and scale invariant Harnack inequality f