Let G be a portion of a C1,a boundary of an n-dimensional domain D. Let u be a solution to a second order parabolic equation in D x (-T, T) and assume that u = 0 on G x (-T, T), 0 G. We prove that u satisfies a three cylinder inequality near G x (-T, T). As a consequence of the previous result we prove that if u (x, t) = O (xk) for every t (-T, T) and every k N, then u is identically equal to zero.

Optimal three cylinder inequality at the boundary for solutions to parabolic equations and unique continuation properties / S. Vessella. - In: ACTA MATHEMATICA SINICA. - ISSN 1439-8516. - STAMPA. - 21:(2005), pp. 351-380. [10.1007/s10114-004-0498-9]

Optimal three cylinder inequality at the boundary for solutions to parabolic equations and unique continuation properties

VESSELLA, SERGIO
2005

Abstract

Let G be a portion of a C1,a boundary of an n-dimensional domain D. Let u be a solution to a second order parabolic equation in D x (-T, T) and assume that u = 0 on G x (-T, T), 0 G. We prove that u satisfies a three cylinder inequality near G x (-T, T). As a consequence of the previous result we prove that if u (x, t) = O (xk) for every t (-T, T) and every k N, then u is identically equal to zero.
2005
21
351
380
S. Vessella
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/327161
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