A priori estimates and unique continuation theorems for second order parabolic equations

Johnson, Raymond

doi:10.1090/S0002-9947-1971-0277897-8

A priori estimates and unique continuation theorems for second order parabolic equations
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Trans. Amer. Math. Soc. 158 (1971), 167-177 Request permission

Abstract:

It is shown that solutions of second-order linear parabolic equations subject to global constraint satisfy an a priori estimate which has among its consequences that if a solution of such an equation vanishes on the characteristic $t = T$ and satisfies the global constraint, it vanishes identically.

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A priori estimates and unique continuation theorems for second-order parabolic equations