In this paper we prove a H¨older propagation of smallness for solutions to second order parabolic equations whose general anisotropic leading coefficient has a jump at an interface. We assume that the leading coefficient is Lipschitz continuous with respect to the parabolic distance on both sides of the interface. The main effort consists in proving a local Carleman estimate for this parabolic operator.

Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface / Francini, Elisa; Vessella, Sergio. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 265:(2018), pp. 2375-2430. [10.1016/j.jde.2018.04.033]

Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface

Francini, Elisa
;
Vessella, Sergio
2018

Abstract

In this paper we prove a H¨older propagation of smallness for solutions to second order parabolic equations whose general anisotropic leading coefficient has a jump at an interface. We assume that the leading coefficient is Lipschitz continuous with respect to the parabolic distance on both sides of the interface. The main effort consists in proving a local Carleman estimate for this parabolic operator.
2018
265
2375
2430
Francini, Elisa; Vessella, Sergio
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1091172
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