Regularity For Solutions Of Nonlocal Fully Nonlinear Parabolic Equations And Free Boundaries On Two Dimensional Cones
Download Regularity For Solutions Of Nonlocal Fully Nonlinear Parabolic Equations And Free Boundaries On Two Dimensional Cones PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Regularity For Solutions Of Nonlocal Fully Nonlinear Parabolic Equations And Free Boundaries On Two Dimensional Cones book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Regularity for Solutions of Nonlocal Fully Nonlinear Parabolic Equations and Free Boundaries on Two Dimensional Cones
On the first part, we consider nonlinear operators I depending on a family of nonlocal linear operators [mathematical equations]. We study the solutions of the Dirichlet initial and boundary value problems [mathematical equations]. We do not assume even symmetry for the kernels. The odd part bring some sort of nonlocal drift term, which in principle competes against the regularization of the solution. Existence and uniqueness is established for viscosity solutions. Several Hölder estimates are established for u and its derivatives under special assumptions. Moreover, the estimates remain uniform as the order of the equation approaches the second order case. This allows to consider our results as an extension of the classical theory of second order fully nonlinear equations. On the second part, we study two phase problems posed over a two dimensional cone generated by a smooth curve [mathematical symbol] on the unit sphere. We show that when [mathematical equation] the free boundary avoids the vertex of the cone. When [mathematical equation]we provide examples of minimizers such that the vertex belongs to the free boundary.
Elliptic and Parabolic Equations Involving the Hardy-Leray Potential
Author: Ireneo Peral Alonso
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2021-02-22
The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
Geometry of PDEs and Related Problems
The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.