Finsler-Rellich inequalities involving the distance to the boundary

Barbatis, G.; Paschalis, M.

doi:10.1090/proc/15800

Finsler-Rellich inequalities involving the distance to the boundary
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by G. Barbatis and M. Paschalis

Proc. Amer. Math. Soc. 150 (2022), 1647-1655

DOI: https://doi.org/10.1090/proc/15800

Published electronically: January 14, 2022

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Abstract:

We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of a half-space we obtain the sharp constant while for a general convex domain we obtain estimates that are better than those obtained by comparison with the polyharmonic operator.

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Proceedings of the American Mathematical Society

Finsler-Rellich inequalities involving the distance to the boundary
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Abstract: