Search results for "Degenerate equation"
showing 3 items of 3 documents
Discontinuous solutions of linear, degenerate elliptic equations
2008
Abstract We give examples of discontinuous solutions of linear, degenerate elliptic equations with divergence structure. These solve positively conjectures of De Giorgi.
Control of essential supremum of solutions of quasilinear degenerate parabolic equations
2001
Sufficient conditions are obtained so that a weak subsolution of a class of quasilinear degenerate parabolic equations, bounded from above on theparabolic boundary of the cylinder Q, turns out to be bounded from above in Q.
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.