This book presents applications of noncommutative and nonassociative algebras to
constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial …

Boundary Harnack Estimates and Quantitative Strong Maximum Principles for Uniformly Elliptic
PDE | International Mathematics Research Notices | Oxford Academic Skip to Main Content …

RIESZ CAPACITY, MAXIMUM PRINCIPLE, AND REMOVABLE SETS OF FULLY
NONLINEAR SECOND-ORDER ELLIPTIC OPERATORS 1. Introduction and mai Page 1 …

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic
type on a manifold X. We study the question: Which closed subsets E⊂ X have the property …

We study the situation in which a solution to a fully nonlinear elliptic equation in a bounded
domain Ω Ω with an overdetermined boundary condition prescribing both Dirichlet and …

Weak Maximum Principle for Degenerate Elliptic Operators in Unbounded Domains |
International Mathematics Research Notices | Oxford Academic Skip to Main Content …

We prove the homogenization of the Dirichlet problem for fully nonlinear uniformly elliptic
operators with periodic oscillation in the operator and in the boundary condition for a …

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 F such that u …

In this article we study the fundamental solutions or “α-harmonic functions” for some
nonlinear positive homogeneous nonlocal elliptic problems in conical domains, such as F …

1. INTRODUCTION. STATEMENT OF THE PROBLEM Let D be an infinite domain in the two-
dimensional space, and let u (P) be a biharmonic function in D continuous up to the …