The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
2021 ◽
Vol 60
(1)
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Keyword(s):
AbstractWe study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, $$\det D u =f$$ det D u = f , where f is integrable and bounded away from zero. In particular, we take $$f\in L^p$$ f ∈ L p , where $$p>1$$ p > 1 , or in $$L\log L$$ L log L . We prove that for a Baire-generic f in either space there are no solutions with the expected regularity.
2017 ◽
Vol 63
(3)
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pp. 475-493
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2003 ◽
Vol 24
(04)
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pp. 529-540
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2012 ◽
Vol 218
(23)
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pp. 11518-11527
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2017 ◽
Vol 66
(6)
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pp. 2187-2204
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2011 ◽
Vol 23
(08)
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pp. 903-931
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