Results 81 to 90 of about 73,971 (227)
On the regularity theory for mixed local and nonlocal quasilinear parabolic equations [PDF]
arXiv, 2021 We consider mixed local and nonlocal quasilinear parabolic equations of $p$-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions, lower semicontinuity of weak supersolutions as well as upper semicontinuity of weak subsolutions. We also discuss the
arxiv
Multiplicative chaos measures from thick points of log‐correlated fields
Communications on Pure and Applied Mathematics, Volume 77, Issue 11, Page 4212-4286, November 2024.Abstract We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires asymptotics of suitable exponential moments for the field. As an application, we establish that these estimates
Janne Junnila +2 more
wiley +1 more source
A topological study for the existence of lower-semicontinuous Richter-Peleg multi-utilities [PDF]
In the present paper we study necessary and sufficient conditions for the existence of a semicontinuous and finite Richter-Peleg multi-utility for a preorder. It is well know that, given a preorder on a topological space, if there is a lower (upper) semicontinuous Richter-Peleg multi-utility, then the topology of the space must be finer than the Upper (
arxiv +1 more source
Mathematical analysis of a mesoscale model for multiphase membranes
GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.Abstract In this article, we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author (Arch. Ration. Mech. Anal. 193, 2009) for the one‐phase case.
Jakob Fuchs, Matthias Röger
wiley +1 more source
About extension of upper semicontinuous multi-valued maps and applications [PDF]
arXiv, 2008 We formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal subset) of a completely normal (resp.
arxiv
Existence of solutions to k‐Wave models of nonlinear ultrasound propagation in biological tissue
Studies in Applied Mathematics, Volume 153, Issue 4, November 2024.Abstract We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k‐Wave. The systems are solved for the acoustic particle velocity, mass density, and acoustic pressure and involve a fractional absorption operator.
Ben Cox +3 more
wiley +1 more source
Nonautonomous attractors of skew-product flows with digitized driving systems
Electronic Journal of Differential Equations, 2001 The upper semicontinuity and continuity properties of pullback attractors for nonautonomous differential equations are investigated when the driving system of the generated skew-product flow is digitized.
R. A. Johnson, Peter E. Kloeden
doaj
On the upper semicontinuity of global attractors for damped wave equations
AIMS Mathematics, 2017 We provide a new proof of the upper-semicontinuity property for the global attractorsadmitted by the solution operators associated with some strongly damped wave equations.
Joseph L. Shomberg
doaj +1 more source
Mathematics, 2020 In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed.
Jing-Nan Li, San-Hua Wang, Yu-Ping Xu
doaj +1 more source
Upper semismooth functions and the subdifferential determination property [PDF]
arXiv, 2017 In this paper, an upper semismooth function is defined to be a lower semicontinuous function whose radial subderivative satisfies a mild directional upper semicontinuity property. Examples of upper semismooth functions are the proper lower semicontinuous convex functions, the lower-C$^1$ functions, the regular directionally Lipschitz functions, the ...
arxiv