Generalized Dirichlet forms and harmonic maps

Calculus of Variations and Partial Differential Equations

Volumn 5, Issue 1, 1996, Pages 1-19

  Jost, Jürgen ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003000207     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050056     Document Type: Article

References (28)

1. [A1] S.I. Al'ber, On n-dimensional problems in the calculus of variations in the large. Sov. Math. Dokl. 5 (1964), 700-704
2. [A2] S.I. Al'ber, Spaces of mappings into a manifold with negative curvature. Sov. Math. Dokl. 9 (1967), 6-9
3. [BD1] A. Beurling and J. Deny, Espaces de Dirichlet I, le cas élémentaire. Acta Math. 99 (1958), 203-224
4. [BD2] A. Beurling and J. Deny, Dirichlet spaces. Proc. Nat. Acad. Sci. USA 45 (1959), 208-215
5. [BM] M. Biroli and U. Mosco, A Saint-Venant type principle for Dirichlet forms on discontinuous media, Annali Mat. Pura Appl. (to appear)
6. [BN] V.N. Berestovskij, I.G. Nikolaev, Multidimensional generalized Riemannian spaces. Encyclopaedia Math. Sciences Vol. 70, Geometry IV (ed. Yu. G. Reshetnyak), Springer (1993), 246-362
7. [C] K. Corlette, Flat G-Bundles with canonical metrics, J. Diff. Geom. 28 (1988), 361-382
8. [Ca] L. Caffarelli, Regularity theorems for weak solutions of some nonlinear systems, Comm. Pure Appl. Math. 35 (1982), 833-838
9. [D] S. Donaldson, Twisted harmonic maps and the self-duality equations, Proc. London Math. Soc. 55 (1987), 127-131
10. [DO] K. Diederich, T. Ohsawa, Harmonic mappings and disk bundles over compact Kähler manifolds Publ. Res. Inst. Math. Sci. 21 (1985), 819-833
11. [FOT] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet forms and symmetric Markov processes, de Gruyter (1994)
12. [GG] M. Giaquinta, E. Giusti, On the regularity of the minima of variational integrals. Acta Math. 148 (1982), 31-46
13. [GH] M. Giaquinta, St. Hildebrandt, A priori estimates for harmonic mappings, J. reine angew. Math. 336 (1982), 124-164
14. [GS] M. Gromov, R. Schoen, Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one, Publ. Math. IHES 76 (1992), 165-246
15. [Hm] R. Hamilton, Harmonic maps of manifolds with boundary Springer L.N.M. 471 (1975)
16. [Hr] P. Hartman, On homotopic harmonic maps. Can. J. Math. 19 (1967), 673-687
17. [J1] J. Jost, Equilibrium maps between metric spaces, Calc. Var. 2 (1994), 173-204
18. [J2] J. Jost, Convex functionals and genralized harmonic maps into spaces of nonpositive curvature, Comment. Math. Helv. 70 (1995), 659-673
19. [J3] J. Jost, Generalized harmonic maps between metric spaces, in: Geometric analysis and the calculus of variations (J. Jost, ed.), International Press, 1996, pp. 143-174
20. [JX] J. Jost, C.J. Xu, Subelliptic harmonic maps, to appear in Trans. AMS
21. [JY] J. Jost, S.T. Yau, Harmonic maps and group representations. Differential Geometry and Minimal Submanifolds (B. Lawson and K. Tenenblat, eds.), Longman Scientific (1991), 241-260
22. [K] W. Kendall, Convexity and the hemisphere J. London, Math. Soc. (2) 43 (1991), 567-576
23. [KS] N. Korevaar, R. Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993), 561-569
24. [La] F. Labourie, Existence d'applications harmoniques tordues à valeurs dans les variétés à courbure négative, Proc. AMS 111 (1991), 877-882
25. [M] M. Meier, On quasilinear elliptic systems with quadratic growth, (preprint)
26. [N] I. Nikolaev, Synthetic methods in Riemannian geometry, Lecture Notes
27. [Re] Y.G. Reshetnyak, Inextensible mappings in a space of curvature no greater than K Siberian Math. Journ. 9 (1968), 683-689
28. [St] K.Th. Sturm, Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations, (preprint)