A Dirichlet problem involving the divergence operator

Csató, G.; Dacorogna, B.

doi:10.1016/j.anihpc.2015.01.006

Csató, G.; Dacorogna, B.

Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 3, pp. 829-848.

Abstract

We consider the problem

{\begin{matrix} div u + 〈 a; u 〉 = f & in Ω \\ u = u_{0} & on \partial Ω . \end{matrix}

We show that if

curl a (x_{0}) \neq 0

for some

x_{0} \in Ω

, then the problem is solvable without restriction on f. We also discuss the regularity of the solution.

MR Zbl

DOI: 10.1016/j.anihpc.2015.01.006

Keywords: Poincaré type lemma, Divergence operator, Boundary value problem

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     author = {Csat\'o, G. and Dacorogna, B.},
     title = {A {Dirichlet} problem involving the divergence operator},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {829--848},
     publisher = {Elsevier},
     volume = {33},
     number = {3},
     year = {2016},
     doi = {10.1016/j.anihpc.2015.01.006},
     zbl = {1338.35106},
     mrnumber = {3489636},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.01.006/}
}

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Csató, G.; Dacorogna, B. A Dirichlet problem involving the divergence operator. Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 3, pp. 829-848. doi : 10.1016/j.anihpc.2015.01.006. http://www.numdam.org/articles/10.1016/j.anihpc.2015.01.006/

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