Real analytic boundary regularity of the Cauchy kernel on convex domains
نویسندگان
چکیده
منابع مشابه
Spectral gap for the Cauchy process on convex, symmetric domains
Let D ⊂ R be a bounded convex domain which is symmetric relative to both coordinate axes. Assume that [−a, a] × [−b, b], a ≥ b > 0 is the smallest rectangle (with sides parallel to the coordinate axes) containing D. Let {λn}n=1 be the eigenvalues corresponding to the semigroup of the Cauchy process killed upon exiting D. We obtain the following estimate on the spectral gap: λ2 − λ1 ≥ Cb a2 , wh...
متن کاملAnalytic regularity of a free boundary problem
In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most n− 8. Mathematics Subject Classification (2000): 49Q20
متن کاملBoundary Value Problems and Regularity on Polyhedral Domains
We prove a well-posedness result for second order boundary value problems in weighted Sobolev spaces on curvilinear polyhedral domains in Rn with Dirichlet boundary conditions. Our typical weight is the distance to the set of singular boundary points.
متن کاملBoundary Behaviour on Convex Domains of Finite Type
We describe the optimal approach regions for a theorem of Fatou type for H p functions on convex domains of nite type in C n. Moreover we show that the Nagel-Stein phenomenon also holds in this context.
متن کاملR . D . Carmichael ANALYTIC FUNCTIONS , CAUCHY KERNEL , AND CAUCHY INTEGRAL IN TUBES
Analytic functions in tubes in association with ultradistributional boundary values are analyzed. Conditions are stated on the analytic functions satisfying a certain norm growth which force the functions to be in the Hardy space H2 . Properties of the Cauchy kernel and Cauchy integral are obtained which extend results obtained previously by the author and collaborators.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1990-1000149-2