2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103846We 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 $τ\in[0,1]$.11 pagesAnalysis of PDEs35J60text