Abstract
In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of $\mathbb R^N$, with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in $(W^{1,q}(\Omega))'$, when $q <N/(N-1)$. The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.
Citation
Jérôme Droniou. "Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method." Adv. Differential Equations 5 (10-12) 1341 - 1396, 2000. https://doi.org/10.57262/ade/1356651226
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