an:04080240
Zbl 0661.47042
Heurteaux, Yanick
Boundary Harnack inequalities for parabolic operators
FR
C. R. Acad. Sci., Paris, S??r. I 308, No. 13, 401-404 (1989).
00155059
1989
j
47F05 35K20
boundary point; parabolic operator; positive L-solutions; boundary Harnack principle; parabolic boundary
Let \(\Omega\) be an open set of \({\mathbb{R}}^{n+1}\) and let Q be a boundary point of \(\Omega\) having a neighborhood whose intersection with the boundary of \(\Omega\) is ``Lipschitz''. For a parabolic operator, we compare the behavior of positive L-solutions in \(\Omega\) converging to zero at every point of the boundary which is sufficiently close to Q. A boundary Harnack principle is then proved and used to describe the cone of positive L-solutions converging to zero at every point of \(\partial_ p\Omega -\{Q\}\), where \(\partial_ p\Omega\) is the parabolic boundary of \(\Omega\).