On the best Hoelder exponent for two dimensional elliptic equations in divergence form
| dc.creator | Ricciardi, Tonia | |
| dc.date | 2005-10-27 | |
| dc.date.accessioned | 2026-07-07T06:48:01Z | |
| dc.date.available | 2026-07-07T06:48:01Z | |
| dc.description | We obtain an estimate for the Hölder continuity exponent for weak solutions to the following elliptic equation in divergence form: \[ \mathrm{div}(A(x)\nabla u)=0 \qquad\mathrm{in\}Ω, \] where $Ω$ is a bounded open subset of $\R^2$ and, for every $x\inΩ$, $A(x)$ 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 $τ\in[0,1]$ we construct coefficient matrices $A_τ$ such that $A_0$ is isotropic and $A_1$ has unit determinant, and such that our estimate for $A_τ$ reduces to an equality, for every $τ\in[0,1]$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510606 | |
| dc.identifier | http://arxiv.org/abs/math/0510606 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103846 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60 | |
| dc.title | On the best Hoelder exponent for two dimensional elliptic equations in divergence form | |
| dc.type | text |