Fractional BV spaces and first applications to scalar conservation laws
نویسندگان
چکیده
The aim of this paper is to obtain new fine properties of entropy solutions of nonlinear scalar conservation laws. For this purpose, we study some “fractional BV spaces” denoted BV s, for 0 < s ≤ 1, introduced by Love and Young in 1937. The BV s(R) spaces are very closed to the critical Sobolev space W s,1/s(R). We investigate these spaces in relation with one-dimensional scalar conservation laws. BV s spaces allow to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions ∗Université de Savoie, LAMA, UMR CNRS 5127, 73376 Le Bourget-du-Lac, [email protected] †Université de Savoie, LAMA, UMR CNRS 5127, 73376 Le Bourget-du-Lac, [email protected] ‡Université de Nice Sophia Antipolis, Labo. JAD, UMR CNRS 7351, Nice, [email protected] §Team COFFE, INRIA Sohpia-Antipolis Méditérannée, 2004 route des lucioles -BP 93, 06902 SophiaAntipolis, France
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