Prescribing the Jacobian determinant in Sobolev spaces

Ye Dong

doi:10.1016/S0294-1449(16)30185-8

Prescribing the Jacobian determinant in Sobolev spaces

Ye Dong

Ecole Normale Supérieure Paris Saclay

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

Let Ω be a bounded domain in Rⁿ with regular boundary. In this paper, we study the equations of the type det (∇ u (x)) = f in Ω and u (x) = x on ∂Ω where f lies in some Sobolev spaces. We establish some existence and non-existence results. A discussion of general cases is also included.

Original language	English
Pages (from-to)	275-296
Number of pages	22
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	11
Issue number	3
DOIs	https://doi.org/10.1016/S0294-1449(16)30185-8
State	Published - 1 May 1994
Externally published	Yes

Keywords

Jacobian determinant
Sobolev spaces
nonlinear PDE

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10.1016/S0294-1449(16)30185-8

Cite this

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abstract = "Let Ω be a bounded domain in Rn with regular boundary. In this paper, we study the equations of the type det (∇ u (x)) = f in Ω and u (x) = x on ∂Ω where f lies in some Sobolev spaces. We establish some existence and non-existence results. A discussion of general cases is also included.",

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AB - Let Ω be a bounded domain in Rn with regular boundary. In this paper, we study the equations of the type det (∇ u (x)) = f in Ω and u (x) = x on ∂Ω where f lies in some Sobolev spaces. We establish some existence and non-existence results. A discussion of general cases is also included.

KW - Jacobian determinant

KW - Sobolev spaces

KW - nonlinear PDE

UR - https://www.scopus.com/pages/publications/85012294476

U2 - 10.1016/S0294-1449(16)30185-8

DO - 10.1016/S0294-1449(16)30185-8

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 3

ER -

Prescribing the Jacobian determinant in Sobolev spaces

Abstract

Keywords

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