In this paper we prove the higher differentiability in the scale of Besov spaces of the solutions to a class of obstacle problems of the type min∫ΩF(x,z,Dz):z∈Kψ(Ω). Here Ω is an open bounded set of Rn, n≥2, ψ is a fixed function called obstacle and Kψ(Ω) is set of admissible functions z∈W1,p(Ω) such that z≥ψ a.e. in Ω. We assume that the gradient of the obstacle belongs to a suitable Besov space. The main novelty here is that we are not assuming any differentiability on the partial maps x↦F(x,z,Dz) and z↦F(x,z,Dz), but only their Hölder continuity.

Regularity results for a class of non-differentiable obstacle problems / Eleuteri, M.; Passarelli di Napoli, A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 194:(2020), pp. 111-434. [10.1016/j.na.2019.01.024]

Regularity results for a class of non-differentiable obstacle problems

Eleuteri M.;Passarelli di Napoli A.
2020

Abstract

In this paper we prove the higher differentiability in the scale of Besov spaces of the solutions to a class of obstacle problems of the type min∫ΩF(x,z,Dz):z∈Kψ(Ω). Here Ω is an open bounded set of Rn, n≥2, ψ is a fixed function called obstacle and Kψ(Ω) is set of admissible functions z∈W1,p(Ω) such that z≥ψ a.e. in Ω. We assume that the gradient of the obstacle belongs to a suitable Besov space. The main novelty here is that we are not assuming any differentiability on the partial maps x↦F(x,z,Dz) and z↦F(x,z,Dz), but only their Hölder continuity.
2020
19-feb-2019
194
111
434
Regularity results for a class of non-differentiable obstacle problems / Eleuteri, M.; Passarelli di Napoli, A.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 194:(2020), pp. 111-434. [10.1016/j.na.2019.01.024]
Eleuteri, M.; Passarelli di Napoli, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1208835
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