Carleman estimates for singular parabolic equations with interior degeneracy and non-smooth coefficients

Advances in Nonlinear Analysis

Mugnai Dimitri¹  Fragnelli Genni² 

[1]Dipartimento di Matematica e Informatica, Università di Perugia,Via Vanvitelli 1, 06123 Perugia, Italy

[2]Dipartimento di Matematica, Università di Bari ”Aldo Moro”, Via E. Orabona 4,70125 Bari, Italy

关键词: carleman estimates;    singular/degenerate equations;    non-smooth coefficients;    hardy–poincaréinequality;    caccioppoli inequality;    observability inequality;    null controllability;    35q93;    93b05;    93b07;    34h15;    35a23;    35b99;   

DOI  :  10.1515/anona-2015-0163

来源: DOAJ

【 摘 要 】

We establish Carleman estimates for singular/degenerate parabolic Dirichlet problems with degeneracy and singularity occurring in the interior of the spatial domain. Our results are completely new, since this situation is not covered by previous contributions for degeneracy and singularity on the boundary. In addition, we consider non-smooth coefficients, thus preventing the use of standard calculations in this framework.

【 授权许可】

Unknown