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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2017
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| 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 |
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| Sumario: | 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. |
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