Archiv der Mathematik

, Volume 98, Issue 4, pp 341-353

First online:

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

  • Robin NittkaAffiliated withMax Planck Institute for Mathematics in the Sciences Email author 

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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


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