On the best Hoelder exponent for two dimensional elliptic equations in divergence form

Details On the best Hoelder exponent for two dimensional elliptic equations in divergence form On the best Hoelder exponent for two dimensional elliptic equations in divergence form

2005-10-27

arxiv.org/abs/math/0510606v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

We obtain an estimate for the H\"older continuity exponent for weak solutions to the following elliptic equation in divergence form: \[ \mathrm{div}(A(x)\nabla u)=0 \qquad\mathrm{in\}\Omega, \] where $\Omega$ is a bounded open subset of $\R^2$ and, for every $x\in\Omega$, $A(x)$ is a matrix with bounded measurable coefficients. Such an estimate "interpolates" between the well-known estimate of Piccinini and Spagnolo in the isotropic case $A(x)=a(x)I$, where $a$ is a bounded measurable function, and our previous result in the unit determinant case $\det A(x)\equiv1$. Furthermore, we show that our estimate is sharp. Indeed, for every $\tau\in[0,1]$ we construct coefficient matrices $A_\tau$ such that $A_0$ is isotropic and $A_1$ has unit determinant, and such that our estimate for $A_\tau$ reduces to an equality, for every $\tau\in[0,1]$.

Affiliated with

Also associated with

No associations

Rating

On the best Hoelder exponent for two dimensional elliptic equations in divergence form 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 On the best Hoelder exponent for two dimensional elliptic equations in divergence form, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the best Hoelder exponent for two dimensional elliptic equations in divergence form will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-322911