Single phase energy minimizers for materials with nonlocal spatial dependence

Quarterly of Applied Mathematics

Volumn 54, Issue 1, 1996, Pages 161-195

  Fosdick, Roger L ^a   Mason, Darren E ^a  

^a University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001429265     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1373845     Document Type: Article

References (15)

1. S. S. Antman, Monotonicity and invertibility conditions in one dimensional nonlinear elasticity. In: Nonlinear Elasticity, Proceedings of a Symposium Conducted by the Mathematics Research Center, University of Wisconsin-Madison, ed. by R. W. Dickey, Academic Press, 1973, pp. 57-92
2. S. S. Antman, Ordinary differential equations of nonlinear elasticity II: Existence and regularity theory for conservative boundary value problems. Arch. Rational Mech. Anal. 61, 353-393 (1976)
3. J. Carr, M. E. Gurtin, and M. Slemrod, Structured phase transitions on a finite interval, Arch. Rational Mech. Anal. 86, 317-351 (1984)
4. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. I, John Wiley and Sons, 1962
5. B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, 1989
6. J. E. Dunn and R. L. Fosdick, The morphology and stability of material phases, Arch. Rational Mech. Anal. 74, 1-99 (1980)
7. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. Studies in Mathematics and its Applications, Volume I, North-Holland Publishing Co., 1976
8. J. L. Ericksen, Equilibrium of Bars, J. Elasticity 5, 191-201 (1975)
9. R. L. Fosdick and D. E. Mason, Energy Minimizers in Nonlocal Continuum Mechanics (Work in progress)
10. T. Lin and R. C. Rogers, Computation of Phase Transitions Using Nonlocal Regularization, ICAM Report, Virginia Polytechnic Institute, Department of Mathematics, 14 September 1993
11. I. Stakgold, Boundary Value Problems of Mathematical Physics, Vol. I, The Macmillan Company, 1967
12. J. D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. (In Dutch), Verhandel. Konink. Akad. Weten. Amsterdam (Sect. 1), 1, No. 8 (1893)
13. J. W. Walter, On a Nonlocal Model of Fluid Phases, Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics, 1985
14. R. L. Wheeden and A. Zygmund, Measure and Integral: An Introduction to Real Analysis, Marcel Dekker, Inc., 1977
15. K. Yosida, Functional Analysis, Springer-Verlag, 1965