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초록· 키워드
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We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map.
The proof is based on Young measures.
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참고문헌 (17)
참고문헌 신청
B. Dacorogna / 2008 / Direct methods in the calculus of variations, Second edition / Springer
C. Villani / 2003 / Topics in Optimal Transportation / Graduate Studies in Mathematics 58
G. Buttazzo / 1989 / Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Research Notes in Mathematics Series, 207. Longman Scientific & Tech
H. Berliocchi / 1973 / Int´egrandes normales et mesures param´etr´ees en calcul des variations / Bull. Soc. Math. France 101 : 129 ~ 184
J. Ball / 1976 / Convexity conditions and existence theorems in nonlinear elasticity / Arch. Rational Mech. Anal. 63 (4) : 337 ~ 403
C. Villani / 2003 / Topics in Optimal Transportation / Graduate Studies in Mathematics 58
G. Buttazzo / 1989 / Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Pitman Research Notes in Mathematics Series, 207. Longman Scientific & Tech
H. Berliocchi / 1973 / Int´egrandes normales et mesures param´etr´ees en calcul des variations / Bull. Soc. Math. France 101 : 129 ~ 184
J. Ball / 1976 / Convexity conditions and existence theorems in nonlinear elasticity / Arch. Rational Mech. Anal. 63 (4) : 337 ~ 403
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