Maps and fields with compressible density

Thomas H. Otway

Rendiconti del Seminario Matematico della Università di Padova (2004)

  • Volume: 111, page 133-159
  • ISSN: 0041-8994

How to cite


Otway, Thomas H.. "Maps and fields with compressible density." Rendiconti del Seminario Matematico della Università di Padova 111 (2004): 133-159. <>.

author = {Otway, Thomas H.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {133-159},
publisher = {Seminario Matematico of the University of Padua},
title = {Maps and fields with compressible density},
url = {},
volume = {111},
year = {2004},

AU - Otway, Thomas H.
TI - Maps and fields with compressible density
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2004
PB - Seminario Matematico of the University of Padua
VL - 111
SP - 133
EP - 159
LA - eng
UR -
ER -


  1. [A] M. ARA, Geometry of F-harmonic maps, Kodai Math. J., 22 (1999), pp. 243-263. Zbl0941.58010MR1700595
  2. [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. Zbl56.1057.01JFM56.1057.01
  3. [Be] L. BERS, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958. Zbl0083.20501MR96477
  4. [Ch] C. J. CHAPMAN, High SpeedFlow, Cambridge University Press, Cambridge, 2000. Zbl0948.76001MR1753394
  5. [CF] G-Q. CHEN - M. FELDMAN, Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type, preprint. Zbl1015.35075MR1969202
  6. [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. Zbl0662.58013MR945880
  7. [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. Zbl0539.35027MR709038
  8. [DO] G. DONG - B. OU, Subsonic flows around a body in space, Commun. Partial Differential Equations, 18 (1993), pp. 355-379. Zbl0813.35013MR1211737
  9. [Ed] D. G. B. EDELEN, Applied Exterior Calculus, Wiley, New York, 1985. Zbl1101.58301MR816136
  10. [EL] J. EELLS - L. LEMAIRE, Some properties of exponentially harmonic maps, Proc. Banach Center, Semester on PDE, 27 (1990), pp. 127-136. Zbl0799.58021
  11. [EP] J. EELS - J. C. POLKING, Removable singularities of harmonic maps, Indiana Univ. Math. J., 33, No. 6 (1984), pp. 859-871. Zbl0559.58011MR763946
  12. [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. Zbl0508.35036MR672713
  13. [F] M. FUCHS, Topics in the Calculus of Variations, Vieweg, Wiesbaden, 1994. Zbl0834.49019MR1320049
  14. [FH] N. FUSCO - J. HUTCHINSON, Partial regularity for minimisers of certain functionals having nonquadratic growth, Ann. Mat. Pura Appl. 155 (1989), pp. 1-24. Zbl0698.49001MR1042826
  15. [G] M. GIAQUINTA, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Theory, Princeton University Press, Princeton, 1983. Zbl0516.49003MR717034
  16. [GT] D. GILBARG - N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
  17. [HL] R. HARDT - F.-H. LIN, Mappings minimizing the Lp norm of the gradient, Commun. Pure Appl. Math., 40 (1987), pp. 555-588. Zbl0646.49007MR896767
  18. [HJW] S. HILDEBRANDT - J. JOST - K.-O. WIDMAN, Harmonic mappings and minimal surfaces, Inventiones Math., 62 (1980), pp. 269-298. Zbl0446.58006MR595589
  19. [ISS] T. IWANIEC - C. SCOTT - B. STROFFOLINI, Nonlinear Hodge theory on manifolds with boundary, Annali Mat. Pura Appl. (4), 177 (1999), pp. 37-115. Zbl0963.58003MR1747627
  20. [J] J. JOST, Riemannian Geometry and Geometric Analysis, SpringerVerlag, Berlin, 1995. Zbl0828.53002MR1351009
  21. [KFL] A. D. KANFON - A. FÜZFA - D. LAMBERT, Some examples of exponentially harmonic maps, arXiv:math-ph/0205021. Zbl1045.58009MR1945767
  22. [LU] O. A. LADYZHENSKAYA - N. N. URAL’TSEVA, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  23. [Le] J. L. LEWIS, Regularity of the derivatives of solutions to certain degenerate elliptic equations, Indiana Univ. Math. J., 32 (1983), pp. 849-858. Zbl0554.35048MR721568
  24. [Li] G. LIAO, A regularity theorem for harmonic maps with small energy, J. Differential Geometry, 22 (1985), pp. 233-241. Zbl0619.58015MR834278
  25. [LM] E. LOUBEAU - S. MONTALDO, A note on exponentially harmonic morphisms, Glasgow Math. J., 42 (2000), pp. 25-29. Zbl0946.58016MR1739695
  26. [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. Zbl0618.58017MR865424
  27. [MTW] C. W. MISNER - K. S. THORNE - J. A. WHEELER, Gravitation, Freeman, New York, 1973. MR418833
  28. [Mo] C. B. MORREY, Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. Zbl0142.38701MR202511
  29. [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. Zbl0974.58018MR1773064
  30. [O2] T. H. OTWAY, Uniformly and nonuniformly elliptic variational equations with gauge invariance, arXiv:math-ph/0007028. 
  31. [SaU] J. SACKS - K. UHLENBECK, The existence of minimal immersions of 2-spheres, Ann. of Math. (2), 113 (1981), pp. 1-24. Zbl0462.58014MR604040
  32. [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. Zbl0551.58011MR765241
  33. [ScU] R. SCHOEN - K. UHLENBECK, A regularity theory for harmonic maps, J. Diff. Geom., 17 (1982), pp. 307-335. Zbl0521.58021MR664498
  34. [Sed] V. I. SEDOV, Introduction to the Mechanics of a Continuous Medium, Addison-Wesley, Reading, 1965. Zbl0123.40502
  35. [Se] J. SERRIN, Local behavior of solutions of quasilinear equations, Acta Math., 111 (1964), pp. 247-302. Zbl0128.09101MR170096
  36. [Sh] M. SHIFFMAN, On the existence of subsonic flows of a compressible fluid, J. Rat. Mech. Anal., 1 (1952), pp. 605-652. Zbl0048.19301MR51651
  37. [Si] L. M. SIBNER, An existence theorem for a nonregular variational problem, Manuscripta Math., 43 (1983), pp. 45-72. Zbl0534.58022MR706801
  38. [SS1] L. M. SIBNER - R. J. SIBNER, A nonlinear Hodge-de Rham theorem, Acta Math., 125 (1970), pp. 57-73. Zbl0216.45703MR281231
  39. [SS2] L. M. SIBNER - R. J. SIBNER, Nonlinear Hodge theory: Applications, Advances in Math., 31 (1979), pp. 1-15. Zbl0408.58032MR521463
  40. [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. Zbl0474.35022MR628593
  41. [Sm] P. D. SMITH, Nonlinear Hodge theory on punctured Riemannian manifolds, Indiana Univ. Math. J., 31, No. 4 (1982), pp. 553-577. Zbl0513.58005MR662917
  42. [So] C. F. SOPUERTA, Applications of timelike and null congruences to the construction of cosmological models, Ph.D. Thesis, Universitat de Barcelona, 1996. 
  43. [T] G. E. TANYI, On the critical points of the classical elastic energy functional, Afrika Matematika, 1 (1978), pp. 35-43. Zbl0513.73007MR566406
  44. [U] K. K. UHLENBECK, Regularity for a class of nonlinear elliptic systems, Acta Math., 138 (1977), pp. 219-240. Zbl0372.35030MR474389

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.