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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  

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Cyclic Homology and the Atiyah-Patodi-Singer Index Theorem

, 2002
We apply the boundary pseudodifferential calculus of Melrose to study the Chern character in entire cyclic homology of the Dirac operator of a manifold with boundary. Recently, Melrose has proved the Atiyah-Patodi-Singer index theorem using a calculus of
E. Getzler
semanticscholar   +1 more source