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Nonlinear Measure Data Problems

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Abstract

We describe some basic results from regularity theory for solutions to elliptic quasilinear equations involving an assigned measure datum and we include some new integrability and differentiability results for sublinear problems.

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  1. Dipartimento di Matematica, Università di Parma, Viale G. P. Usberti 53/a, Campus, I-43100, Parma, Italy

    Giuseppe Mingione

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  1. Giuseppe Mingione
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Correspondence to Giuseppe Mingione.

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To Lucio Boccardo on his mth birthday, $${m \in}$$ (60, 65)

This work has been supported by the ERC grant 207573 “Vectorial problems”.

Lecture held in the Seminario Matematico e Fisico di Milano on March 4, 2010

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Mingione, G. Nonlinear Measure Data Problems. Milan J. Math. 79, 429–496 (2011). https://doi.org/10.1007/s00032-011-0168-1

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