Zobrazeno 1 - 10
of 379
pro vyhledávání: '"35s15"'
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
This paper introduces a new pseudodifferential preconditioner for the Helmholtz equation in variable media with absorption. The pseudodifferential operator is associated with the multiplicative inverse to the symbol of the Helmholtz operator. This ap
Externí odkaz:
http://arxiv.org/abs/2409.16172
Autor:
Sampedro, Juan Carlos
In this paper we use abstract bifurcation theory for Fredholm operators of index zero to deal with periodic even solutions of the one-dimensional equation $\mathcal{L}u=\lambda u+|u|^{p}$, where $\mathcal{L}$ is a nonlocal pseudodifferential operator
Externí odkaz:
http://arxiv.org/abs/2409.04253
Autor:
Ervin, V. J.
In this paper we analyze the existence, uniqueness and regularity of the solution to the generalized, variable diffusivity, fractional Laplace equation on the unit disk in $\mathbb{R}^{2}$. For $\alpha$ the order of the differential operator, our res
Externí odkaz:
http://arxiv.org/abs/2405.02457
Autor:
Kreisbeck, Carolin, Schönberger, Hidde
This work revolves around properties and applications of functions whose nonlocal gradient, or more precisely, finite-horizon fractional gradient, vanishes. Surprisingly, in contrast to the classical local theory, we show that this class forms an inf
Externí odkaz:
http://arxiv.org/abs/2402.11308
We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications of our re
Externí odkaz:
http://arxiv.org/abs/2401.18033
To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows u
Externí odkaz:
http://arxiv.org/abs/2312.09080
The aim of this paper is investigating the existence and multiplicity of weak solutions to non--local equations involving the {\em magnetic fractional Laplacian}, when the nonlinearity is subcritical and asymptotically linear at infinity. We prove ex
Externí odkaz:
http://arxiv.org/abs/2312.04473
Autor:
Abels, Helmut, Grubb, Gerd
We prove optimal regularity results in $L_p$-based function spaces in space and time for a large class of linear parabolic equations with a nonlocal elliptic operator in bounded domains with limited smoothness. Here the nonlocal operator is given by
Externí odkaz:
http://arxiv.org/abs/2312.01864
Let $u_s$ denote a solution of the fractional Poisson problem $$ (-\Delta)^s u_s = f\quad\text{ in }\Omega,\qquad u_s=0\quad \text{ on }\mathbb{R}^N\setminus \Omega, $$ where $N\geq 2$ and $\Omega\subset \mathbb{R}^N$ is a bounded domain of class $C^
Externí odkaz:
http://arxiv.org/abs/2311.18476