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

Advances in Nonlinear Analysis

article

Genni Fragnelli¹  Dimitri Mugnai² 

[1]Dipartimento di Matematica, Università di Bari ”Aldo Moro”

[2]Dipartimento di Matematica e Informatica, Università di Perugia

关键词: Carleman estimates;    singular/degenerate equations;    non-smooth coefficients;    Hardy–Poincaréinequality;    Caccioppoli inequality;    observability inequality;    null controllability;   

DOI  :  10.1515/anona-2015-0163

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 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】

CC BY