Maps and fields with compressible density
Otway, Thomas H.
Rendiconti del Seminario Matematico della Università di Padova, Tome 111 (2004), p. 133-159 / Harvested from Numdam
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@article{RSMUP_2004__111__133_0,
     author = {Otway, Thomas H.},
     title = {Maps and fields with compressible density},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {111},
     year = {2004},
     pages = {133-159},
     mrnumber = {2076737},
     zbl = {1121.76056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2004__111__133_0}
}

Otway, Thomas H. Maps and fields with compressible density. Rendiconti del Seminario Matematico della Università di Padova, Tome 111 (2004) pp. 133-159. http://gdmltest.u-ga.fr/item/RSMUP_2004__111__133_0/

[A] M. Ara, Geometry of F-harmonic maps, Kodai Math. J., 22 (1999), pp. 243-263. | MR 1700595 | Zbl 0941.58010

[Ba] H. Bateman, Notes on a differential equation which occurs in the twodimensional motion of a compressible fluid and the associated variational problem, Proc. R. Soc. London Ser. A, 125 (1929), pp. 598-618. | JFM 56.1057.01

[Be] L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958. | MR 96477 | Zbl 0083.20501

[Ch] C. J. Chapman, High Speed Flow, Cambridge University Press, Cambridge, 2000. | MR 1753394 | Zbl 0948.76001

[CF] G-Q. Chen - M. Feldman, Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type, preprint. | MR 1969202 | Zbl 1015.35075

[CL] D. Costa - G. Liao, On removability of a singular submanifold for weakly harmonic maps, J. Fac. Sci. Univ. Tokyo Sect. 1A Math., 35 (1988), pp. 321-344. | MR 945880 | Zbl 0662.58013

[D] E. Dibenedetto, C11a local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis T. M. A., 7, No. 8 (1983), pp. 827-850. | MR 709038 | Zbl 0539.35027

[DO] G. Dong - B. Ou, Subsonic flows around a body in space, Commun. Partial Differential Equations, 18 (1993), pp. 355-379. | MR 1211737 | Zbl 0813.35013

[Ed] D. G. B. Edelen, Applied Exterior Calculus, Wiley, New York, 1985. | MR 816136 | Zbl 1101.58301

[EL] J. Eells - L. Lemaire, Some properties of exponentially harmonic maps, Proc. Banach Center, Semester on PDE, 27 (1990), pp. 127-136. | Zbl 0799.58021

[EP] J. Eels - J. C. Polking, Removable singularities of harmonic maps, Indiana Univ. Math. J., 33, No. 6 (1984), pp. 859-871. | MR 763946 | Zbl 0559.58011

[Ev] L. C. Evans, A new proof of local C11a regularity for solutions of certain degenerate elliptic P.D.E., J. Differential Equations, 45 (1982), pp. 356-373. | MR 672713 | Zbl 0508.35036

[F] M. Fuchs, Topics in the Calculus of Variations, Vieweg, Wiesbaden, 1994. | MR 1320049 | Zbl 0834.49019

[FH] N. Fusco - J. Hutchinson, Partial regularity for minimisers of certain functionals having nonquadratic growth, Ann. Mat. Pura Appl. 155 (1989), pp. 1-24. | MR 1042826 | Zbl 0698.49001

[G] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Theory, Princeton University Press, Princeton, 1983. | MR 717034 | Zbl 0516.49003

[GT] D. Gilbarg - N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[HL] R. Hardt - F.-H. Lin, Mappings minimizing the Lp norm of the gradient, Commun. Pure Appl. Math., 40 (1987), pp. 555-588. | MR 896767 | Zbl 0646.49007

[HJW] S. Hildebrandt - J. Jost - K.-O. Widman, Harmonic mappings and minimal surfaces, Inventiones Math., 62 (1980), pp. 269-298. | MR 595589 | Zbl 0446.58006

[ISS] T. Iwaniec - C. Scott - B. Stroffolini, Nonlinear Hodge theory on manifolds with boundary, Annali Mat. Pura Appl. (4), 177 (1999), pp. 37-115. | MR 1747627 | Zbl 0963.58003

[J] J. Jost, Riemannian Geometry and Geometric Analysis, SpringerVerlag, Berlin, 1995. | MR 1351009 | Zbl 0828.53002

[KFL] A. D. Kanfon - A. Füzfa - D. Lambert, Some examples of exponentially harmonic maps, arXiv:math-ph/0205021. | MR 1945767 | Zbl 1045.58009

[LU] O. A. Ladyzhenskaya - N. N. Ural'Tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. | MR 244627 | Zbl 0164.13002

[Le] J. L. Lewis, Regularity of the derivatives of solutions to certain degenerate elliptic equations, Indiana Univ. Math. J., 32 (1983), pp. 849-858. | MR 721568 | Zbl 0554.35048

[Li] G. Liao, A regularity theorem for harmonic maps with small energy, J. Differential Geometry, 22 (1985), pp. 233-241. | MR 834278 | Zbl 0619.58015

[LM] E. Loubeau - S. Montaldo, A note on exponentially harmonic morphisms, Glasgow Math. J., 42 (2000), pp. 25-29. | MR 1739695 | Zbl 0946.58016

[Me] M. Meier, Removable singularities of harmonic maps and an application to minimal submanifolds, Indiana Univ. Math. J., 35, No. 4 (1986), pp. 705-726. | MR 865424 | Zbl 0618.58017

[MTW] C. W. Misner - K. S. Thorne - J. A. Wheeler, Gravitation, Freeman, New York, 1973. | MR 418833

[Mo] C. B. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. | MR 202511 | Zbl 0142.38701

[O1] T. H. Otway, Nonlinear Hodge maps, J. Math. Phys., 41, No. 8 (2000), pp. 5745-5766. A slightly revised version of this paper is posted at arXiv:math-ph/9908030. | MR 1773064 | Zbl 0974.58018

[O2] T. H. Otway, Uniformly and nonuniformly elliptic variational equations with gauge invariance, arXiv:math-ph/0007028.

[SaU] J. Sacks - K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. of Math. (2), 113 (1981), pp. 1-24. | MR 604040 | Zbl 0462.58014

[Sch] R. Schoen, Analytic aspects of the harmonic map problem, in: S. S. Chern, ed., Seminar on Nonlinear Partial Differential Equations, Springer-Verlag, New York, 1985, pp. 321-358. | MR 765241 | Zbl 0551.58011

[ScU] R. Schoen - K. Uhlenbeck, A regularity theory for harmonic maps, J. Diff. Geom., 17 (1982), pp. 307-335. | MR 664498 | Zbl 0521.58021

[Sed] V. I. Sedov, Introduction to the Mechanics of a Continuous Medium, Addison-Wesley, Reading, 1965. | Zbl 0123.40502

[Se] J. Serrin, Local behavior of solutions of quasilinear equations, Acta Math., 111 (1964), pp. 247-302. | MR 170096 | Zbl 0128.09101

[Sh] M. Shiffman, On the existence of subsonic flows of a compressible fluid, J. Rat. Mech. Anal., 1 (1952), pp. 605-652. | MR 51651 | Zbl 0048.19301

[Si] L. M. Sibner, An existence theorem for a nonregular variational problem, Manuscripta Math., 43 (1983), pp. 45-72. | MR 706801 | Zbl 0534.58022

[SS1] L. M. Sibner - R. J. Sibner, A nonlinear Hodge-de Rham theorem, Acta Math., 125 (1970), pp. 57-73. | MR 281231 | Zbl 0216.45703

[SS2] L. M. Sibner - R. J. Sibner, Nonlinear Hodge theory: Applications, Advances in Math., 31 (1979), pp. 1-15. | MR 521463 | Zbl 0408.58032

[SS3] L. M. Sibner - R. J. Sibner, A sub-elliptic estimate for a class of invariantly defined elliptic systems, Pacific J. Math., 94, No. 2 (1982), pp. 417-421. | MR 628593 | Zbl 0474.35022

[Sm] P. D. Smith, Nonlinear Hodge theory on punctured Riemannian manifolds, Indiana Univ. Math. J., 31, No. 4 (1982), pp. 553-577. | MR 662917 | Zbl 0513.58005

[So] C. F. Sopuerta, Applications of timelike and null congruences to the construction of cosmological models, Ph.D. Thesis, Universitat de Barcelona, 1996.

[T] G. E. Tanyi, On the critical points of the classical elastic energy functional, Afrika Matematika, 1 (1978), pp. 35-43. | MR 566406 | Zbl 0513.73007

[U] K. K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta Math., 138 (1977), pp. 219-240. | MR 474389 | Zbl 0372.35030