[图书][B] Integro-differential elliptic equations

X Fernández-Real, X Ros-Oton - 2024 - Springer
Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …

Obstacle problems for nonlocal operators with singular kernels

X Ros-Oton, M Weidner - arXiv preprint arXiv:2308.01695, 2023 - arxiv.org
In this paper we establish optimal regularity estimates and smoothness of free boundaries
for nonlocal obstacle problems governed by a very general class of integro-differential …

Generic properties in free boundary problems

X Fernández-Real, H Yu - arXiv preprint arXiv:2308.13209, 2023 - arxiv.org
In this work, we show the generic uniqueness of minimizers for a large class of energies,
including the Alt-Caffarelli and Alt-Phillips functionals. We then prove the generic regularity …

Epiperimetric inequalities in the obstacle problem for the fractional Laplacian

M Carducci - Calculus of Variations and Partial Differential …, 2024 - Springer
Using epiperimetric inequalities approach, we study the obstacle problem min {(-Δ) su, u-φ}=
0, for the fractional Laplacian (-Δ) s with obstacle φ∈ C k, γ (R n), k≥ 2 and γ∈(0, 1). We …

An epiperimetric inequality for odd frequencies in the thin obstacle problem

M Carducci, B Velichkov - arXiv preprint arXiv:2409.12110, 2024 - arxiv.org
We prove an epiperimetric inequality for the thin obstacle Weiss' energy with odd
frequencies and we apply it to solutions to the thin obstacle problem with general …

Obstacle Problems

X Fernández-Real, X Ros-Oton - Integro-Differential Elliptic Equations, 2024 - Springer
In this chapter, we study obstacle problems for nonlocal elliptic operators. In order to do so,
we first prove the boundary Harnack inequality for such operators in Lipschitz domains, a …

[图书][B] Statistical Mechanics of Log and Riesz Interactions

L Peilen - 2023 - search.proquest.com
We study the statistical mechanics of the log-gas, or β-ensemble, for general potential and
inverse temperature. By means of a bootstrap procedure, we prove local laws on the next …

[PDF][PDF] The fractional obstacle problem

X FernánDez-reaL - REAL SOCIEDAD MATEMÁTICA … - academica-e.unavarra.es
The fractional obstacle problem Page 15 15 | CONFERENCIAS PLENARIAS THE
FRACTIONAL OBSTACLE PROBLEM Xavier FernánDez-reaL Institute of Mathematics …