Zobrazeno 1 - 10
of 563
pro vyhledávání: '"35R09"'
Autor:
Grube, Florian
We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional Laplacian.
Externí odkaz:
http://arxiv.org/abs/2410.00829
Autor:
Liao, Naian, Weidner, Marvin
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we show that
Externí odkaz:
http://arxiv.org/abs/2409.20097
Autor:
Hivert, Hélène, Salin, Florian
In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion equation by inc
Externí odkaz:
http://arxiv.org/abs/2409.18629
We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincar\'e inequalities. When the order of fractional differentiability goes to $0$ or $1$, we recover the weighted Lebesgue and Sobol
Externí odkaz:
http://arxiv.org/abs/2409.11829
Autor:
Vougalter, Vitali
We prove the existence of stationary solutions for some systems of reaction-diffusion type equations with superdiffusion in the corresponding H^2 spaces. Our method is based on the fixed point theorem when the elliptic problems contain first order di
Externí odkaz:
http://arxiv.org/abs/2409.09507
We study the regularity of weak solutions to nonlocal in time subdiffusion equations for a wide class of weakly singular kernels appearing in the generalised fractional derivative operator. We prove a weak Harnack inequality for nonnegative weak supe
Externí odkaz:
http://arxiv.org/abs/2409.04841
In this work, we investigate the generalized bathtub model, a nonlocal transport equation for describing network trip flows served by privately operated vehicles inside a road network. First, we establish the well-posedness of the mathematical model
Externí odkaz:
http://arxiv.org/abs/2409.00619
We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in $L^\infty$ in the case of hard potentials. As a consequence, we derive $
Externí odkaz:
http://arxiv.org/abs/2408.03067
Autor:
Huan, Ling, Romani, Giulio
We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser. For all prescribed values of the mass, we prove existence of a positiv
Externí odkaz:
http://arxiv.org/abs/2407.20618
Autor:
Acquistapace, Paolo, Bucci, Francesca
We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on the LQ probl
Externí odkaz:
http://arxiv.org/abs/2407.15559