An Extension Problem Related to the Fractional Laplacian
نویسندگان
چکیده
منابع مشابه
An extension problem related to the fractional Laplacian
The operator square root of the Laplacian (−△) can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this paper we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some proper...
متن کاملAn Extension Problem for the Cr Fractional Laplacian
We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre.
متن کاملLogical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem
Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...
متن کاملAn overdetermined problem in Riesz-potential and fractional Laplacian
The main purpose of this paper is to address two open questions raised by Reichel (2009) in [2] on characterizations of balls in terms of the Riesz potential and fractional Laplacian. For a bounded C1 domainΩ ⊂ RN , we consider the Riesz-potential u(x) = ∫ Ω 1 | x− y |N−α dy for 2 ≤ α = N . We show that u = constant on ∂Ω if and only if Ω is a ball. In the case of α = N , the similar characteri...
متن کاملTHE BREZIS-NIRENBERG PROBLEM FOR THE FRACTIONAL p-LAPLACIAN
We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when p 6= 2. We get around this difficulty by working with certain...
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: Communications in Partial Differential Equations
سال: 2007
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300600987306