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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2018

DENSITY ESTIMATES FOR DEGENERATE DOUBLE-WELL POTENTIALS

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Résumé

We consider a general energy functional for phase coexistence models, which comprises the case of Banach norms in the gradient term plus a double-well potential. We establish density estimates for Q-minima. Namely, the state parameters close to both phases are proved to occupy a considerable portion of the ambient space. From this, we obtain the uniform convergence of the level sets to the limit interface in the sense of Hausdorff distance. The main novelty of these results lies in the fact that we do not assume the double-well potential to be nondegenerate in the vicinity of the minima. As far as we know, these types of density results for degenerate potentials are new even for minimizers and even in the case of semilinear equations, but our approach can comprise at the same time quasilinear equations, Q-minima, and general energy functionals.

Dates et versions

hal-03621414 , version 1 (28-03-2022)

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Serena Dipierro, Alberto Farina, Enrico Valdinoci. DENSITY ESTIMATES FOR DEGENERATE DOUBLE-WELL POTENTIALS. SIAM Journal on Mathematical Analysis, 2018, 50 (6), pp.6333-6347. ⟨10.1137/17M114933X⟩. ⟨hal-03621414⟩
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