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Annali di Matematica Pura ed Applicata

, Volume 106, Issue 1, pp 11–38 | Cite as

Sul problema di Dirichlet per equazioni paraboliche del secondo ordine a coefficienti discontinui

  • Ermanno Lanconelli
Article

Summary

We consider Dirichlet problem for a class of parabolic operators with discontinuous coefficients having the form
$$Lu = \sum\limits_{i = 1}^n {\frac{\partial }{{\partial x_i }}\left[ {\sum\limits_{j = 1}^n {a_{ij} (z)\frac{{\partial u}}{{\partial x_j }}} + a_i (z)u} \right]} + \sum\limits_{i = 1}^n {b_i (z)} \frac{{\partial u}}{{\partial x_i }} + c(z)u - \frac{{\partial u}}{{\partial y}}$$
. We prove some necessary and sufficient conditions for a boundary point to be regular for every operator of this kind.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Ermanno Lanconelli
    • 1
  1. 1.Bologna

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