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Global integrability for minimizers of anisotropic functionals

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Abstract

We consider integral functionals in which the density has growth p i with respect to \({\frac{\partial u}{\partial x_i}}\), like in

$$\int\limits_{\Omega}\left( \left| \frac{\partial u}{\partial x_1}(x) \right|^{p_1} + \left|\frac{\partial u}{\partial x_2}(x)\right|^{p_2} + \cdots + \left|\frac{\partial u}{\partial x_n}(x) \right|^{p_n} \right) dx.$$

We show that higher integrability of the boundary datum forces minimizer to be more integrable.

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Authors and Affiliations

  1. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, 67100, L’Aquila, Italy

    Francesco Leonetti

  2. Via Grillo 12, 84080, Pellezzano, SA, Italy

    Francesco Siepe

Authors
  1. Francesco Leonetti
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  2. Francesco Siepe
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Correspondence to Francesco Leonetti.

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We acknowledge the support of MIUR.

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Leonetti, F., Siepe, F. Global integrability for minimizers of anisotropic functionals. manuscripta math. 144, 91–98 (2014). https://doi.org/10.1007/s00229-013-0641-y

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