The equation divu + 〈a,u〉 = f
2019 ◽
Vol 22
(04)
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pp. 1950035
Keyword(s):
We study the solutions [Formula: see text] to the equation [Formula: see text] where [Formula: see text] and [Formula: see text] are given. We significantly improve the existence results of [G. Csató and B. Dacorogna, A Dirichlet problem involving the divergence operator, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016) 829–848], where this equation has been considered for the first time. In particular, we prove the existence of a solution under essentially sharp regularity assumptions on the coefficients. The condition that we require on the vector field [Formula: see text] is necessary and sufficient. Finally, our results cover the whole scales of Sobolev and Hölder spaces.
2008 ◽
Vol 22
(4)
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pp. 973-987
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2015 ◽
Vol 35
(11)
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pp. 5353-5378
2003 ◽
Vol 106
(2)
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pp. 185-222
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1995 ◽
Vol 51
(2)
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pp. 365-372
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2004 ◽
Vol 17
(1)
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pp. 221-243
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