A spherical Harnack inequality for singular solutions of nonlinear elliptic equations

Chiun-Chuan Chen; Chang-Shou Lin

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2001)

  • Volume: 30, Issue: 3-4, page 713-738
  • ISSN: 0391-173X

How to cite

top

Chen, Chiun-Chuan, and Lin, Chang-Shou. "A spherical Harnack inequality for singular solutions of nonlinear elliptic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 30.3-4 (2001): 713-738. <http://eudml.org/doc/84458>.

@article{Chen2001,
author = {Chen, Chiun-Chuan, Lin, Chang-Shou},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3-4},
pages = {713-738},
publisher = {Scuola normale superiore},
title = {A spherical Harnack inequality for singular solutions of nonlinear elliptic equations},
url = {http://eudml.org/doc/84458},
volume = {30},
year = {2001},
}

TY - JOUR
AU - Chen, Chiun-Chuan
AU - Lin, Chang-Shou
TI - A spherical Harnack inequality for singular solutions of nonlinear elliptic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2001
PB - Scuola normale superiore
VL - 30
IS - 3-4
SP - 713
EP - 738
LA - eng
UR - http://eudml.org/doc/84458
ER -

References

top
  1. [1] G. Bianchi, Nonexistence of positive solutions to semilinear elliptic equations on Rn or Rn+ through the method of moving planes, Comm. Partial Differential Equation22 (1997), 1671-1670. Zbl0910.35048MR1469586
  2. [2] H. Brezis - Y.Y. Li - I. Shafrir, A sup + inf inequality for some nonlinear elliptic equations involving exponential nonlinearities, J. Func. Anal.115 (1993), 34.4.-358. Zbl0794.35048MR1234395
  3. [3] L.A. Caffarelli - B. Gidas - J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev exponent, Comm. Pure Appl. Math.42 (1989),271-297. Zbl0702.35085MR982351
  4. [4] W. Chen - C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J.63 (1991), 615-622. Zbl0768.35025MR1121147
  5. [5] C.C. Chen - C.S. Lin, Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent, Duke Math. J., 78 (1995), 315-334. Zbl0839.35014MR1333503
  6. [6] C.C. Chen - C.S. Lin, On compactness and completeness of conformal metrics in Rn, Asian J. Math.1 (1997), 549-559. Zbl0901.53027MR1604918
  7. [7] C.C. Chen - C.S. Lin, Estimates of the conformal scalar curvature equation via the method of moving planes, Comm. Pure Appl. Math.50 (1997), 971-1017. Zbl0958.35013MR1466584
  8. [8] C.C. Chen - C.S. Lin, On the asymptotic symmetry of singular solutions of the scalar curvature equations, Math. Ann.313 (1999), 229-245. Zbl0927.35034MR1679784
  9. [9] B. Gidas - W.M. Ni - L. Nirenberg, Symmetry of positive solutions of nonlinear equations in Rn, In: "Mathematical Analysis and Applications", part A, pp. 369-402, Advances in Math. Supp. Stud.79, Academic Press, New York-London, 1981. Zbl0469.35052
  10. [10] N. Korevaar - R. Mazzeo - F. Pacard - R. Schoen, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math.135 (1999), 233-272. Zbl0958.53032MR1666838
  11. [11] C. Li, Local asymptotic symmetry of Singular Solutions to Nonlinear Elliptic Equations, Invent. Math.123 (1996), 221-232. Zbl0849.35009MR1374197
  12. [12] Y.Y. Li, Harnack type inequality: the method of moving planes, Comm. Math. Phys.200 (1999), 421-444. Zbl0928.35057MR1673972
  13. [13] C.S. Lin, On Liouville theorem and apriori estimate for the scalar curvature equations, Ann. Scuola. Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), 107-130. Zbl0974.53032MR1658881
  14. [14] C.S. Lin, Estimates of the conformal scalar curvature equation via the method of moving planes III, Comm. Pure Appl. Math.53 (2000), 611-646. Zbl1035.53052MR1737506
  15. [15] R. Mazzeo - F. Pacard, A construction of singular solutions for semilinear elliptic equation using asymptotic analysis, J. Differential Geom.44 (1996), 331-370. Zbl0869.35040MR1425579
  16. [16] D. Pollack, Compactness results for complete metrics of constant positive scalar curvature on of subdomains of Sn' Indiana Univ. Math. J.42 (1993), 1441-1456. Zbl0794.53025MR1266101
  17. [17] R. Schoen, The existence of weak solutions with prescribed singular behavior for a conformal invariant scalar equation, Comm. Pure Appl. Math.41 (1988), 317-392. Zbl0674.35027MR929283
  18. [18] J. Serrin, A symmetry problem in potential theory, Arch. Rat. Mech. Anal.43 (1971), 304-318. Zbl0222.31007MR333220
  19. [19] S.D. Taliaferro, On the growth of superharmonic functions near an isolated singularity I, J. Differential Equations158 (1999), 28-47. Zbl0939.31005MR1721720

NotesEmbed ?

top

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.