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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 $$\Omega$$.

##### MSC:
 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