We consider second-order parabolic equations with time indepen- dent coefficients. Under reasonable assumptions, it is known that the fun- damental solution satisfies certain Gaussian bounds related to the associated geodesic distance. In this article we prove a sharp unique continuation property at the initial time which matches exactly the above-mentioned kernel bounds.
Albano P., Tataru D. (2004). Unique continuation for second-order parabolic operators at the initial time. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 132, 1077-1085 [10.1090/S0002-9939-03-07227-7].
Unique continuation for second-order parabolic operators at the initial time
ALBANO, PAOLO;
2004
Abstract
We consider second-order parabolic equations with time indepen- dent coefficients. Under reasonable assumptions, it is known that the fun- damental solution satisfies certain Gaussian bounds related to the associated geodesic distance. In this article we prove a sharp unique continuation property at the initial time which matches exactly the above-mentioned kernel bounds.File in questo prodotto:
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