Abstract
We establish Weiss and Monneau’s type quasi-monotonicity formulas for quadratic energies having a matrix of coefficients in a Sobolev space with summability exponent larger than the space dimension. We provide applications to the free boundary analysis for the corresponding classical obstacle problems first, and then for nonlinear classical obstacle problems thanks to a linearization argument
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Acknowledgements
E. S. has been supported by the ERC-STG Grant no. 759229 HiCoS “Higher Co-dimension Singularities: Minimal Surfaces and the Thin Obstacle Problem.” M. F., F. G. and E. S. are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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Focardi, M., Geraci, F., Spadaro, E. (2021). Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applications. In: Mariano, P.M. (eds) Variational Views in Mechanics. Advances in Mechanics and Mathematics(), vol 46. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-90051-9_7
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DOI: https://doi.org/10.1007/978-3-030-90051-9_7
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