Hölder Estimates for Singular Non-local Parabolic Equations

Details Hölder Estimates for Singular Non-local Parabolic Equations Hölder Estimates for Singular Non-local Parabolic Equations

2011-05-17

arxiv.org/abs/1105.3286v1

Mathematics

Analysis of PDEs

34 pages

Scientific paper

In this paper, we establish local H\"older estimate for non-negative solutions of the singular equation \eqref{eq-nlocal-PME-1} below, for $m$ in the range of exponents $(\frac{n-2\sigma}{n+2\sigma},1)$. Since we have trouble in finding the local energy inequality of $v$ directly. we use the fact that the operator $(-\La)^{\sigma}$ can be thought as the normal derivative of some extension $v^{\ast}$ of $v$ to the upper half space, \cite{CS}, i.e., $v$ is regarded as boundary value of $v^{\ast}$ the solution of some local extension problem. Therefore, the local H\"older estimate of $v$ can be obtained by the same regularity of $v^{\ast}$. In addition, it enables us to describe the behaviour of solution of non-local fast diffusion equation near their extinction time.

Affiliated with

Also associated with

No associations

Rating

Hölder Estimates for Singular Non-local Parabolic Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hölder Estimates for Singular Non-local Parabolic Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hölder Estimates for Singular Non-local Parabolic Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727671