Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms

@inproceedings{Grenon2017ExistenceAA,
  title={Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms},
  author={Nathalie Grenon and François Murat and Alessio Porreta},
  year={2017}
}
In this Note we prove an a priori estimate and the existence of a solution for a class of nonlinear elliptic problems whose model is −div A(x)Du+α0u = γ|Du|q + f(x), when 1 < q < 2 andf ∈ Lm(Ω) for some suitablem. The main interest of the result lies in the a priori estimate, the complete proof of which is given in the Note. c © XXXX Académie des sciences/ Éditions scientifiques et médicales Elsevier SAS Existence et estimation a priori pour des probl èmes elliptiques avec des termes sous… CONTINUE READING
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