Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation

Yoshinori Morimoto[1]; Chao-Jiang Xu[2]

  • [1] Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501, Japan
  • [2] Université de Rouen, UMR 6085-CNRS, Mathématiques, 76821 Mont-Saint-Aignan, France

Séminaire Équations aux dérivées partielles (2003-2004)

  • Volume: 2003-2004, page 1-14

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Morimoto, Yoshinori, and Xu, Chao-Jiang. "Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation." Séminaire Équations aux dérivées partielles 2003-2004 (2003-2004): 1-14. <http://eudml.org/doc/11096>.

@article{Morimoto2003-2004,
affiliation = {Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501, Japan; Université de Rouen, UMR 6085-CNRS, Mathématiques, 76821 Mont-Saint-Aignan, France},
author = {Morimoto, Yoshinori, Xu, Chao-Jiang},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-14},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation},
url = {http://eudml.org/doc/11096},
volume = {2003-2004},
year = {2003-2004},
}

TY - JOUR
AU - Morimoto, Yoshinori
AU - Xu, Chao-Jiang
TI - Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation
JO - Séminaire Équations aux dérivées partielles
PY - 2003-2004
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2003-2004
SP - 1
EP - 14
LA - eng
UR - http://eudml.org/doc/11096
ER -

References

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  2. M. Derridj, Un problème aux limites pour une classe d’opérateurs du second ordre hypoelliptiques, Annales de l’Institut Fourier21 (1971), 99–148. Zbl0215.45405
  3. D. Jerison, The Dirichlet problem for the Kohn-Laplacian on the Heisenberg group, Parts I and II, J. Funct. Analysis, 43 (1981), 97–142. Zbl0493.58021MR639800
  4. H. Kumano-go, Pseudo-differential operators, MIT Press, 1982 Zbl0489.35003
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  7. Y. Morimoto, A criterion for hypoellipticity of second order differential operators, Osaka J. Math.24 (1987), 651-675. Zbl0644.35023MR923880
  8. Y. Morimoto and T. Morioka, The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators, Bull. Sc. Math.121 (1997) , 507-547. Zbl0891.35025MR1485327
  9. Y. Morimoto and T. Morioka, Hypoellipticity for elliptic operators with infinite degeneracy, “Partial Differential Equations and Their Applications” (Chen Hua and L. Rodino, eds.), World Sci. Publishing, River Edge, NJ, (1999), 240-259. Zbl0992.35026
  10. Y. Morimoto and C.-J. Xu, Logarithmic Sobolev inequality and semi-linear Dirichlet problems for infinitely degenerate elliptic operators, Astérisque284 (2003), 245–264. Zbl1096.35048MR2003422
  11. Y. Morimoto and C.-J. Xu, Nonlinear hypoellipticity of infinite type, Preprint, 2003. Zbl1251.35022MR2332078
  12. C.-J. Xu, The Dirichlet problems for a class of semilinear sub-elliptic equations. Nonlinear Anal.37 (1999), no. 8, Ser. A: Theory Methods, 1039–1049. Zbl0942.35086MR1689283
  13. C.-J. Xu, Nonlinear microlocal analysis. General theory of partial differential equations and microlocal analysis (Trieste, 1995), 155–182, Pitman Res. Notes Math. Ser., 349, Longman, Harlow, 1996. Zbl0861.35150MR1429636
  14. C.-J. Xu, Regularity problem for quasi-linear second order subelliptic equations, Comm. Pure Appl. Math.,45 77–96 (1992). Zbl0827.35023
  15. C.-J. Xu and C. Zuily , Smoothness up to the boundary for solutions of the nonlinear and nonelliptic Dirichlet problem, Trans. Amer. Math. Soc.,308 (1988), 243–257. Zbl0669.35019MR946441

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