This manuscript aims to provide a self-contained introduction to the regularity theory for
elliptic PDE, focusing on the main ideas rather than proving all results in their greatest …

We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl
group H n, whose prototype is the Dirichlet problem for the p-fractional subLaplace equation …

As a first result we prove higher order Schauder estimates for solutions to
singular/degenerate elliptic equations of type-div ρ a A∇ w= ρ af+ div ρ a F in Ω for …

We prove the parabolic boundary Harnack inequality in parabolic flat Lipschitz domains by
blow-up techniques, allowing, for the first time, a non-zero right-hand side. Our method …

We study viscosity solutions to the classical one-phase problem and its thin counterpart. In
low dimensions, we show that when the free boundary is the graph of a continuous function …

We give Martin representation of nonnegative functions caloric with respect to the fractional
Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean …

Aim of this paper is to provide higher order boundary Harnack principles (De Silva and
Savin, 2015 [13]) for elliptic equations in divergence form under Dini type regularity …

We obtain a global extension of the classical weak Harnack inequality which extends and
quantifies the Hopf–Oleinik boundary-point lemma, for uniformly elliptic equations in …

In this work we establish the optimal regularity for solutions to the fully nonlinear thin
obstacle problem. In particular, we show the existence of an optimal exponent $\alpha_F …

arXiv:2304.03624v1 [math.AP] 7 Apr 2023 Page 1 arXiv:2304.03624v1 [math.AP] 7 Apr 2023
BOUNDARY BEHAVIOR OF SOLUTIONS TO FRACTIONAL p-LAPLACIAN EQUATION …