Published Paper

Inserted: 28 mar 2025
Last Updated: 28 mar 2025

Journal: J. Elliptic Parabol. Equ.
Year: 2020
Doi: 10.1007/s41808-020-00088-4

Abstract:

This paper deals with the Lipschitz continuity of solutions to variational obstacle problems with nearly linear growth. The main tool used here is a new higher differentiability result which reveals to be crucial because it allows us to perform the linearization procedure to transform the constrained problem in an unconstrained one and it permits us to deduce the equivalence between our minimization problem and its corresponding variational formulation. Our results hold true for a large class of example for which the Lavrentiev phenomenon does not occur, not necessarily for lagrangians dependent on the modulus of the gradient. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.

Keywords: obstacle problems, Nearly linear growth, regularity of solutions, a-priori estimates

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• Bertazzoni_Riccò_2020.pdf