Prescribing the Jacobian determinant in Sobolev spaces
作者： Ye Dong
DOI: 10.1016/S0294-1449(16)30185-8
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摘要: Abstract Let Ω be a bounded domain in R n with regular boundary. In this paper, we study the equations of type det (∇ u ( x )) = f and ) on ∂Ω where lies some Sobolev spaces. We establish existence non-existence results. A discussion general cases is also included.
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sci-hub.se 参考文章(12)
Elias M. Stein, Singular Integrals and Differentiability Properties of Functions. ,(1971)
Jacques Louis Lions, Problèmes aux limites dans les équations aux dérivées partielles Les Presses de L'Université de Montréal.. ,(1965)
J. M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 88, pp. 315- 328 ,(1981) , 10.1017/S030821050002014X
J.P Bourguignon, H Brezis, Remarks on the Euler equation Journal of Functional Analysis. ,vol. 15, pp. 341- 363 ,(1974) , 10.1016/0022-1236(74)90027-5
Patricia Bauman, Nicholas Owen, Daniel Phillips, Maximum principles and a priori estimates for an incompressible material in nonlinear elasticity Communications in Partial Differential Equations. ,vol. 17, pp. 1185- 1212 ,(1992) , 10.1080/03605309208820882
P. LeTallec, J. T. Oden, Existence and characterization of hydrostatic pressure in finite deformations of incompressible elastic bodies Journal of Elasticity. ,vol. 11, pp. 341- 357 ,(1981) , 10.1007/BF00058078
A I Shnirel'man, ON THE GEOMETRY OF THE GROUP OF DIFFEOMORPHISMS AND THE DYNAMICS OF AN IDEAL INCOMPRESSIBLE FLUID Mathematics of The Ussr-sbornik. ,vol. 56, pp. 79- 105 ,(1987) , 10.1070/SM1987V056N01ABEH003025
John M. Ball, Convexity conditions and existence theorems in nonlinear elasticity Archive for Rational Mechanics and Analysis. ,vol. 63, pp. 337- 403 ,(1976) , 10.1007/BF00279992
Bernard Dacorogna, Jürgen Moser, On a partial differential equation involving the Jacobian determinant Annales De L Institut Henri Poincare-analyse Non Lineaire. ,vol. 7, pp. 1- 26 ,(1990) , 10.1016/S0294-1449(16)30307-9
J{ürgen Moser, On the volume elements on a manifold Transactions of the American Mathematical Society. ,vol. 120, pp. 286- 294 ,(1965) , 10.1090/S0002-9947-1965-0182927-5