Archiv der Mathematik

, Volume 98, Issue 4, pp 341–353

Projections onto convex sets and L p -quasi-contractivity of semigroups

Authors

    • Max Planck Institute for Mathematics in the Sciences
Article

DOI: 10.1007/s00013-012-0374-2

Cite this article as:
Nittka, R. Arch. Math. (2012) 98: 341. doi:10.1007/s00013-012-0374-2

Abstract

Based on a simple geometric description of orthogonal projections onto closed, convex sets we find an implicit formula for the L 2-projection onto the L p -unit ball. This allows us to to prove the L p -quasi-contractivity of semigroups generated by linear elliptic operators and quasi-linear operators of q-Laplace-type in a simple way.

Mathematics Subject Classification

Primary 35K15 Secondary 35B45

Keywords

Semigroup L p -contraction Orthogonal projection Maximal regularity Quasi-linear equations p(x)-Laplace

Copyright information

© Springer Basel AG 2012