Area Formulas for σ-Harmonic Mappings

作者: Giovanni Alessandrini , Vincenzo Nesi

DOI: 10.1007/978-1-4615-0777-2_1

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摘要: The goal of the present paper is two-fold. First, we review some recent progress concerning generalizations various classical results, such as sufficient conditions to guarantee univalence harmonic mappings in dimension two, certain pairs elliptic partial differential equations with measurable coefficients. Second, apply these results prove new area formulas which are valid for a large class arising solutions equations. Finally, briefly discuss applications homogenized constants context G-closure problems. To Professor Olga A. Ladyzhenskaya our deep admiration

参考文章(65)
Grégoire Allaire, Véronique Lods, Minimizers for a double-well problem with affine boundary conditions Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 129, pp. 439- 466 ,(1999) , 10.1017/S0308210500021454
Richard Snyder Laugesen, Injectivity can fail for higher-dimensional harmonic extensions Complex Variables and Elliptic Equations. ,vol. 28, pp. 357- 369 ,(1996) , 10.1080/17476939608814865
François Murat, Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. ,vol. 8, pp. 69- 102 ,(1981)
V. Nesi, Bounds on the effective conductivity of two-dimensional composites made of n ≧ 3 isotropic phases in prescribed volume fraction: the weighted translation method Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 125, pp. 1219- 1239 ,(1995) , 10.1017/S0308210500030481
V. Nesi, Using quasiconvex functionals to bound the effective conductivity of composite materials Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 123, pp. 633- 679 ,(1993) , 10.1017/S0308210500030894
Giovanni Alessandrini, Vincenzo Nesi, Univalent σ-Harmonic Mappings Archive for Rational Mechanics and Analysis. ,vol. 158, pp. 155- 171 ,(2001) , 10.1007/PL00004242
M. Sigalotti, G. Alessandrini, GEOMETRIC PROPERTIES OF SOLUTIONS TO THE ANISOTROPIC p-LAPLACE EQUATION IN DIMENSION TWO Annales Academiae Scientiarum Fennicae. Mathematica. ,vol. 26, pp. 249- 266 ,(2001)
G. W. Milton, V. Nesi, Optimal G-closure bounds via stability under lamination Archive for Rational Mechanics and Analysis. ,vol. 150, pp. 191- 207 ,(1999) , 10.1007/S002050050186
Sergio Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. ,vol. 21, pp. 657- 699 ,(1967)
Giovanni Alessandrini, Vincenzo Nesi, Univalent -Harmonic Mappings Archive for Rational Mechanics and Analysis. ,vol. 2, pp. 155- 171 ,(2001)