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Abstract:

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.

Registro:

Documento: Artículo
Título:Traces for fractional Sobolev spaces with variable exponents
Autor:Del Pezzo, L.M.; Rossi, J.D.
Filiación:CONICET and Departamento de Matemáticas y Estadística, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, Buenos Aires, C1428BCW, Argentina
CONICET and Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Palabras clave:Fractional operators; p-Laplacian; Variable exponents
Año:2017
Volumen:2
Número:4
Página de inicio:435
Página de fin:446
DOI: http://dx.doi.org/10.22034/aot.1704-1152
Título revista:Advances in Operator Theory
Título revista abreviado:Adv. Oper. Theo.
ISSN:2538225X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_2538225X_v2_n4_p435_DelPezzo

Referencias:

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Citas:

---------- APA ----------
Del Pezzo, L.M. & Rossi, J.D. (2017) . Traces for fractional Sobolev spaces with variable exponents. Advances in Operator Theory, 2(4), 435-446.
http://dx.doi.org/10.22034/aot.1704-1152
---------- CHICAGO ----------
Del Pezzo, L.M., Rossi, J.D. "Traces for fractional Sobolev spaces with variable exponents" . Advances in Operator Theory 2, no. 4 (2017) : 435-446.
http://dx.doi.org/10.22034/aot.1704-1152
---------- MLA ----------
Del Pezzo, L.M., Rossi, J.D. "Traces for fractional Sobolev spaces with variable exponents" . Advances in Operator Theory, vol. 2, no. 4, 2017, pp. 435-446.
http://dx.doi.org/10.22034/aot.1704-1152
---------- VANCOUVER ----------
Del Pezzo, L.M., Rossi, J.D. Traces for fractional Sobolev spaces with variable exponents. Adv. Oper. Theo. 2017;2(4):435-446.
http://dx.doi.org/10.22034/aot.1704-1152