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Lipschitz properties in variable exponent problems via relative rearrangement

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Abstract

The author first studies the Lipschitz properties of the monotone and relative rearrangement mappings in variable exponent Lebesgue spaces completing the result given in [9]. This paper is ended by establishing the Lipschitz properties for quasilinear problems with variable exponent when the right-hand side is in some dual spaces of a suitable Sobolev space associated to variable exponent.

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Authors and Affiliations

  1. UMR 6086 CNRS. Laboratoire de Mathématiques, Université de Poitiers, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, BP30179, 86962, Futuroscope Chasseneuil Cedex, France

    Jean-Michel Rakotoson

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  1. Jean-Michel Rakotoson
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Correspondence to Jean-Michel Rakotoson.

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Dedicated to Professor Roger Temam on the Occasion of his 70th Birthday

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Rakotoson, JM. Lipschitz properties in variable exponent problems via relative rearrangement. Chin. Ann. Math. Ser. B 31, 991–1006 (2010). https://doi.org/10.1007/s11401-010-0608-1

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