Related papers: Free Boundary Problems: The Forefront of Current a…
The interior free boundary theory for linear elliptic operators in higher dimensions was developed by Caffarelli in the low regularity context. In these notes, the up-to-the boundary free boundary regularity is discussed for nonlinear…
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is…
An account is given on newest developments on $p$-adic boundary value problems on $p$-adic analytic manifolds and their relationship with diffusion. In particular, novel coordinate Laplacians on $p$-adic analytic $n$-manifolds constructed…
In this paper we numerically research the solutions of the phase field system for the spherically symmetric Stefan-Gibbs-Thomson problem in the case of interaction of the free boundaries. We analyze the effect of the soliton type…
This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…
This Resource Letter treats the nascent discipline of physical eschatology, which deals with the future evolution of astrophysical objects, including the universe itself, and is thus both a counterpart and a complement to conventional…
We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy…
The purpose of these notes is describe the state of progress on the restriction problem in harmonic analysis, with an emphasis on the developments of the past decade or so on the Euclidean space version of these problems for spheres and…
Over the last decade, researchers and engineers have developed a vast body of methodologies and technologies in requirements engineering for self-adaptive systems. Although existing studies have explored various aspects of this topic, few…
Recent successes in the Machine Learning community have led to a steep increase in the number of papers submitted to conferences. This increase made more prominent some of the issues that affect the current review process used by these…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
We prove the -- to the best knowledge of the authors -- first result on the fine asymptotic behavior of the regular part of the free boundary of the obstacle problem close to singularities. The result is motivated by our recent partial…
The paper surveys open problems and questions related to interplay between the theory of integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis geometry. This text has grown out from preparatory materials for…
There have been rapid advancements in the capabilities of large language models (LLMs) in recent years, greatly revolutionizing the field of natural language processing (NLP) and artificial intelligence (AI) to understand and interact with…
Researchers have attempted to model information diffusion and topic trends and lifecycle on online social networks. They have investigated the role of content, social connections and communities, familiarity and behavioral similarity in…
In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are…
A few topics beyond the standard model are reviewed.
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond…