JournalsrlmVol. 31, No. 1pp. 191–210

Lipschitz continuity results for a class of obstacle problems

  • Carlo Benassi

    Università degli Studi di Modena e Reggio Emilia, Italy
  • Michele Caselli

    ETH Zürich, Switzerland
Lipschitz continuity results for a class of obstacle problems cover
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Abstract

We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of pp-type, p2p \geq 2. The main novelty is the use of a linearization technique going back to [28] in order to interpret our constrained minimizer as a solution to a nonlinear elliptic equation, with a bounded right hand side. This lead us to start a Moser iteration scheme which provides the LL^\infty bound for the gradient. The application of a recent higher differentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowdledge, this is the first result for non-automonous functionals with standard growth conditions in the direction of the Lipschitz regularity.

Cite this article

Carlo Benassi, Michele Caselli, Lipschitz continuity results for a class of obstacle problems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 191–210

DOI 10.4171/RLM/885