Estimates for the gradient of solutions of nonlinear elliptic equations withL 1 data

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We prove estimates for the gradient of solutions u of the homogeneous Dirichlet problem for an equation in the form A(u)=f, where A(u) is a p-laplacian type operator and f is a summable function. The estimate on |Du| is obtained via an estimate on its rearrangement.


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Work partially supported by MURST (40%).

Entrata in Redazione il 9 dicembre 1998.

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Alvino, A., Ferone, V. & Trombetti, G. Estimates for the gradient of solutions of nonlinear elliptic equations withL 1 data. Annali di Matematica pura ed applicata 178, 129–142 (2000).

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  • Orlicz Space
  • Isoperimetric Inequality
  • Entropy Solution
  • Lorentz Space
  • Nonlinear Elliptic Equation