Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A class of nonlocal hypoelliptic operators and their extensions (1811.02968v3)

Published 7 Nov 2018 in math.AP

Abstract: In this paper we study nonlocal equations driven by the fractional powers of hypoelliptic operators in the form $$\mathscr K u = \mathscr A u - \partial_t u \overset{def}{=} \operatorname{tr}(Q \nabla2 u) + <BX,\nabla u> - \partial_t u,$$ introduced by H\"ormander in his 1967 hypoellipticity paper. We show that the nonlocal operators $(-\mathscr K)s$ and $(-\mathscr A)s$ can be realized as the Dirichlet-to-Neumann map of doubly-degenerate extension problems. We solve such problems in $L\infty$, and in $Lp$ for $1\leq p<\infty$ when $\operatorname{tr}(B)\geq 0$. In forthcoming works we use such calculus to establish some new Sobolev and isoperimetric inequalities.

Summary

We haven't generated a summary for this paper yet.