Zobrazeno 1 - 10
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pro vyhledávání: '"35d30"'
Autor:
Lee, Haesung
In this paper, we show that, for a solution to the stationary Fokker-Planck equation with general coefficients, defined as a measure with an $L^2$-density, this density not only exhibits $H^{1,2}$-regularity but also H\"{o}lder continuity. To achieve
Externí odkaz:
http://arxiv.org/abs/2412.14636
Autor:
Dutton, Ben, Katzourakis, Nikos
In this paper we study $2$nd order $L^\infty$ variational problems, through seeking to minimise a supremal functional involving the Hessian of admissible functions as well as lower-order terms. Specifically, given a bounded domain $\Omega\subseteq \m
Externí odkaz:
http://arxiv.org/abs/2412.11701
Autor:
Akrami, Seyed Ebrahim
Inspired by quantum mechanics, we introduce a weak form of solutions for differential equations and differential identities like Stokes theorem and Euler-Lagrange equation. We show that Schr\"{o}dinger equation is a weak from of the classical Euler-L
Externí odkaz:
http://arxiv.org/abs/2412.10886
Autor:
Biswas, Reshmi, Quaas, Alexander
This article is concerned regarding the nonexistence of positive solutions for nonlinear fractional elliptic inequalities in exterior domains of $\mathbb R^n$, $n\geq1$. We would like to highlight the fact that our results are new with very weak assu
Externí odkaz:
http://arxiv.org/abs/2412.06746
Undercompressive shocks are a special type of discontinuities that satisfy the viscous profile criterion rather than the Lax inequalities. These shocks can appear as a solution to systems of two or more conservation laws. This paper presents the cons
Externí odkaz:
http://arxiv.org/abs/2412.04439
Autor:
Liu, Songchen
In this article, we solve the complex Monge-Amp\`ere equation for measures with a pluripolar part in compact K\"ahler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the pro
Externí odkaz:
http://arxiv.org/abs/2412.03445
Autor:
Dong, Hongjie, Ryu, Junhee
We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space $\{x_d>0\}$. The leading coefficients are of the form $x_d^2a_{ij}$, where $a_{ij}$ are measurable in $(t,x_d)$ except $a_{dd}$, which is measu
Externí odkaz:
http://arxiv.org/abs/2412.00779
Autor:
Black, Tobias
We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \begin{align*} \left\{ \begin{array}{c@{\quad}l@{\quad}l@{\,}c} n_{t}+u\cdot\nabla n=\nabla\cdot\big(D(n)\nabla n-nS(x,n,c)\cdot\nabla c\big),\ &x\in\Omega,& t>0,\
Externí odkaz:
http://arxiv.org/abs/2411.18336
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively
Externí odkaz:
http://arxiv.org/abs/2411.13444
This paper analyzes a two-by-two Temple-type system of conservation laws with discontinuous flux, focusing on applications in traffic modeling. We prove the existence of entropy solutions for initial data with sufficiently small total variation. Addi
Externí odkaz:
http://arxiv.org/abs/2411.12531