We are interested here in questions related to the regularity of solutions of elliptic problems with Dirichlet or Neumann boundary condition. For the last 30 years, many works have been concerned with questions when Ω is a Lipschitz domain.
We give here some complements for the case of the Laplacian, the Bilaplacian and the operator div (A∇), when A is a matrix or a function, and we extend this study to obtain other regularity results for domains having an adequate regularity.
Using the duality method, we will then revisit the work of Lions-Magenes, concerning the so-called very weak solutions, when the data are less regular. Thanks to the interpolation theory, it permits us to extend the classes of solutions and then to obtain new results of regularity.
| Subject : | : | talk |
| PDF version | : |  PDF version |
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