Results 21 to 26 of about 149 (26)

Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains [PDF]

arXiv, 2011
We prove continuity on domains up to the boundary for n/2-polyharmonic maps into manifolds. Technically, we show how to adapt Helein's direct approach to the fractional setting. This extends a remark by the author that this is possible in the setting of Riviere's famous regularity result for critical points of conformally invariant variational ...
arxiv  

Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise [PDF]

arXiv, 2012
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations with nonlocal interactions), asymptotic methods are offered to solve these equations to obtain ...
arxiv  

Bifurcation and multiplicity results for critical fractional p-Laplacian problems [PDF]

arXiv, 2014
In this paper we investivate bifurcation results for a class of problem in a smooth bounded domain involving the fractional p-Laplacian operator and with a nonlinearity that reaches the critical growth with respect to the fractional Sobolev embedding.
arxiv  

Gelfand-Shilov Regularity of SG Boundary Value Problems [PDF]

arXiv, 2014
We show that the solutions of SG elliptic boundary value problems defined on the complement of compact sets or on the half-space have some regularity in Gelfand-Shilov spaces. The results are obtained using classical results about Gevrey regularity of elliptic boundary value problems and Calder\'on projectors techniques adapted to the SG case.
arxiv  

Boundary regularity and Hopf lemma for nondegenerate stable operators [PDF]

arXiv
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. A Hopf-type boundary lemma is proven, too.
arxiv  

An extension problem of higher order operators and operators of logarithmic type via renormalization [PDF]

arXiv
We introduce a method of obtaining a higher order extension problem, \'a la Caffarelli-Silvestre, utilizing ideas from renormalization. Moreover, we give an alternative perspective of the recently developed extension problem for the logarithmic laplacian developed by Chen, Hauer and Weth (2023) [arXiv:2312.15689].
arxiv