Traces for fractional Sobolev spaces with variable exponents

In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p:Ω×Ω→ (1,∞) and q:∂Ω→(1,1) are continuous functions such that (n - 1)p(x, x)/n - sp(x, x) > q(x) in∂Ω∩x ∈ Ω: n-sp(x, x) > 0), then the inequality fLq(·(∂Ω≤C(fLp(·(Ω)...

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Guardado en:
Detalles Bibliográficos
Publicado: 2017
Materias:
Fractional operators
p-Laplacian
Variable exponents
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_2538225X_v2_n4_p435_DelPezzo
http://hdl.handle.net/20.500.12110/paper_2538225X_v2_n4_p435_DelPezzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_2538225X_v2_n4_p435_DelPezzo
record_format dspace
spelling paper:paper_2538225X_v2_n4_p435_DelPezzo2023-06-08T16:36:49Z Traces for fractional Sobolev spaces with variable exponents Fractional operators p-Laplacian Variable exponents In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p:Ω×Ω→ (1,∞) and q:∂Ω→(1,1) are continuous functions such that (n - 1)p(x, x)/n - sp(x, x) > q(x) in∂Ω∩x ∈ Ω: n-sp(x, x) > 0), then the inequality fLq(·(∂Ω≤C(fLp(·(Ω)+|f|s, p(middot;,middot;) denotes the fractional seminorm with variable exponent, that is given by|f|s, p(middot;,middot;):=inf(λ > 0∫Ω∫Ω |f(x) - f(y)|p(x, y)/λp(x, y)|x-y|n+sp(x, y) dxdy < 1) and f Lq(·)(∂Ω) and f Lp(·)(Ω) are the usual Lebesgue norms with variable exponent. © 2016 by the Tusi Mathematical Research Group. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_2538225X_v2_n4_p435_DelPezzo http://hdl.handle.net/20.500.12110/paper_2538225X_v2_n4_p435_DelPezzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fractional operators
p-Laplacian
Variable exponents
spellingShingle Fractional operators
p-Laplacian
Variable exponents
Traces for fractional Sobolev spaces with variable exponents
topic_facet Fractional operators
p-Laplacian
Variable exponents
description In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if p:Ω×Ω→ (1,∞) and q:∂Ω→(1,1) are continuous functions such that (n - 1)p(x, x)/n - sp(x, x) > q(x) in∂Ω∩x ∈ Ω: n-sp(x, x) > 0), then the inequality fLq(·(∂Ω≤C(fLp(·(Ω)+|f|s, p(middot;,middot;) denotes the fractional seminorm with variable exponent, that is given by|f|s, p(middot;,middot;):=inf(λ > 0∫Ω∫Ω |f(x) - f(y)|p(x, y)/λp(x, y)|x-y|n+sp(x, y) dxdy < 1) and f Lq(·)(∂Ω) and f Lp(·)(Ω) are the usual Lebesgue norms with variable exponent. © 2016 by the Tusi Mathematical Research Group.
title Traces for fractional Sobolev spaces with variable exponents
title_short Traces for fractional Sobolev spaces with variable exponents
title_full Traces for fractional Sobolev spaces with variable exponents
title_fullStr Traces for fractional Sobolev spaces with variable exponents
title_full_unstemmed Traces for fractional Sobolev spaces with variable exponents
title_sort traces for fractional sobolev spaces with variable exponents
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_2538225X_v2_n4_p435_DelPezzo
http://hdl.handle.net/20.500.12110/paper_2538225X_v2_n4_p435_DelPezzo
_version_ 1768546277271797760

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