We prove a Carleman estimate with singular weight for general second order parabolic operators. As a consequence we get an optimal three cylinder inequality for any solution, u, of a second order parabolic equation Lu=0 , in D x(-T,T), where D is a domain of R^n and T is a positive number.
Carleman Estimates, Optimal Three Cylinder Inequality and Unique Continuation Properties for Solutions to Parabolic Equations / S. VESSELLA. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 28:(2003), pp. 637-676. [10.1081/PDE-120020491]
Carleman Estimates, Optimal Three Cylinder Inequality and Unique Continuation Properties for Solutions to Parabolic Equations
VESSELLA, SERGIO
2003
Abstract
We prove a Carleman estimate with singular weight for general second order parabolic operators. As a consequence we get an optimal three cylinder inequality for any solution, u, of a second order parabolic equation Lu=0 , in D x(-T,T), where D is a domain of R^n and T is a positive number.
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