Lipschitz properties in variable exponent problems via relative rearrangement

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.

Keywords

Monotone rearrangement / Relative rearrangement / Variable exponents / Quasi-linear equations

References

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