, Volume 98, Issue 4, pp 341-353
Date: 30 Mar 2012

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

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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.