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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Autores principales: Del Pezzo, L.M., Rossi, J.D.
Formato: JOUR
Materias:
Fractional operators
p-Laplacian
Variable exponents
Acceso en línea: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 todo:paper_2538225X_v2_n4_p435_DelPezzo
record_format dspace
spelling todo:paper_2538225X_v2_n4_p435_DelPezzo2023-10-03T16:42:28Z Traces for fractional Sobolev spaces with variable exponents Del Pezzo, L.M. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Del Pezzo, L.M.
Rossi, J.D.
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.
format JOUR
author Del Pezzo, L.M.
Rossi, J.D.
author_facet Del Pezzo, L.M.
Rossi, J.D.
author_sort Del Pezzo, L.M.
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
url http://hdl.handle.net/20.500.12110/paper_2538225X_v2_n4_p435_DelPezzo
work_keys_str_mv AT delpezzolm tracesforfractionalsobolevspaceswithvariableexponents
AT rossijd tracesforfractionalsobolevspaceswithvariableexponents
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