An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates

In this paper, we establish global Sobolev a priori estimates for Lp-viscosity solutions of fully nonlinear elliptic equations as follows: F(D2u,Du,u,x) = f(x)in Ωu(x) = φ(x) on ∂Ω by considering minimal integrability condition on the data, i.e. f Lp(Ω),φ W2,p(Ω) for n < p < ∞ and a regular do...

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Detalles Bibliográficos
Publicado: 2018
Materias:
fully nonlinear elliptic equations
Global W 2, p and BMO type estimates
relaxed convexity assumptions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DaSilva
http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DaSilva
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02191997_v_n_p_DaSilva
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spelling paper:paper_02191997_v_n_p_DaSilva2023-06-08T15:21:36Z An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates fully nonlinear elliptic equations Global W 2, p and BMO type estimates relaxed convexity assumptions In this paper, we establish global Sobolev a priori estimates for Lp-viscosity solutions of fully nonlinear elliptic equations as follows: F(D2u,Du,u,x) = f(x)in Ωu(x) = φ(x) on ∂Ω by considering minimal integrability condition on the data, i.e. f Lp(Ω),φ W2,p(Ω) for n < p < ∞ and a regular domain Ω ⊂ Rn, and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting "fine" regularity estimates from a limiting operator, the Recession profile, associated to F to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when f p -BMO ⊇ L∞. In such a scenery, we show that solutions admit BMO type estimates for their second derivatives. © 2018 World Scientific Publishing Company. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DaSilva http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DaSilva
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic fully nonlinear elliptic equations
Global W 2, p and BMO type estimates
relaxed convexity assumptions
spellingShingle fully nonlinear elliptic equations
Global W 2, p and BMO type estimates
relaxed convexity assumptions
An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates
topic_facet fully nonlinear elliptic equations
Global W 2, p and BMO type estimates
relaxed convexity assumptions
description In this paper, we establish global Sobolev a priori estimates for Lp-viscosity solutions of fully nonlinear elliptic equations as follows: F(D2u,Du,u,x) = f(x)in Ωu(x) = φ(x) on ∂Ω by considering minimal integrability condition on the data, i.e. f Lp(Ω),φ W2,p(Ω) for n < p < ∞ and a regular domain Ω ⊂ Rn, and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting "fine" regularity estimates from a limiting operator, the Recession profile, associated to F to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when f p -BMO ⊇ L∞. In such a scenery, we show that solutions admit BMO type estimates for their second derivatives. © 2018 World Scientific Publishing Company.
title An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates
title_short An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates
title_full An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates
title_fullStr An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates
title_full_unstemmed An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates
title_sort asymptotic treatment for non-convex fully nonlinear elliptic equations: global sobolev and bmo type estimates
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v_n_p_DaSilva
http://hdl.handle.net/20.500.12110/paper_02191997_v_n_p_DaSilva
_version_ 1768544908793085952

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