Archiv der Mathematik

, Volume 98, Issue 4, pp 341–353

Projections onto convex sets and Lp-quasi-contractivity of semigroups


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


Based on a simple geometric description of orthogonal projections onto closed, convex sets we find an implicit formula for the L2-projection onto the Lp-unit ball. This allows us to to prove the Lp-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 


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

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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