We investigate regularity of the distance function from submanifolds with boundary of Rn. By exploiting these regularity results, we show a Poincaré inequality with matrix weights that degenerate along a submanifold with boundary. Furthermore, we prove uniqueness of solutions to elliptic and parabolic equations which degenerate on submanifolds with boundary.
Distance from submanifolds with boundary and applications to Poincaré inequalities and to elliptic and parabolic problems
Monticelli D. D.;Punzo F.
2019-01-01
Abstract
We investigate regularity of the distance function from submanifolds with boundary of Rn. By exploiting these regularity results, we show a Poincaré inequality with matrix weights that degenerate along a submanifold with boundary. Furthermore, we prove uniqueness of solutions to elliptic and parabolic equations which degenerate on submanifolds with boundary.File in questo prodotto:
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