Regularity of solutions to degenerate $p$-Laplacian equations

Details Regularity of solutions to degenerate $p$-Laplacian equations Regularity of solutions to degenerate $p$-Laplacian equations

2011-10-14

arxiv.org/abs/1110.3295v2

Mathematics

Analysis of PDEs

v2 some revisions. 30 pages

Scientific paper

We prove regularity results for solutions of the equation \[div(< AXu,X u>^{(p-2)/2} AX u) = 0,\] $1\leq \Lambda w(x)^{2/p}|\xi|^2,\] $w \in A_p$, then we show that solutions are locally H\"older continuous. If the degeneracy is of the form \[ k(x)^{-2/p'}|\xi|^2\leq < A(x)\xi,\xi>\leq k(x)^{2/p}|\xi|^2, \] $k\in A_{p'}\cap RH_\tau$,where $\tau$ depends on the homogeneous dimension, then the solutions are continuous almost everywhere, and we give examples to show that this is the best result possible. We give an application to maps of finite distortion.

Affiliated with

Also associated with

No associations

Rating

Regularity of solutions to degenerate $p$-Laplacian 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 Regularity of solutions to degenerate $p$-Laplacian equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Regularity of solutions to degenerate $p$-Laplacian equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-523697