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Boundary Harnack inequalities for parabolic operators. (Inégalités de Harnack à la frontière pour des opérateurs paraboliques.) (French) Zbl 0661.47042
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 \(\Omega\).

47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
35K20 Initial-boundary value problems for second-order parabolic equations