OUHABAZ, El Maati

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OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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Archiv der Mathematik. 2015, vol. 105, p. 79-91

Springer Verlag

Resumen en inglés

We consider the maximal regularity problem for non-autonomous evolution equa-tions u (t) + A(t) u(t) = f (t), t ∈ (0, τ ] u(0) = u 0 . (0.1) Each operator A(t) is associated with a sesquilinear form a(t) on a Hilbert space H. We as-sume that these forms all have the same domain V . It is proved in [11] that if the forms have some regularity with respect to t (e.g., piecewise α-Hölder continuous for some α > 1 /2) then the above problem has maximal Lp–regularity for all u 0 in the real-interpolation space (H, D(A(0))) 1−1/p,p . In this paper we prove that the regularity required there can be im-proved for a class of sesquilinear forms. The forms considered here are such that the difference a(t; ·, ·) − a(s; ·, ·) is continuous on a larger space than the common domain V . We give three examples which illustrate our results.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194575

Proyecto ANR

Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013

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Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251