Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation
Morimoto, Yoshinori1 ; Xu, Chao-Jiang2
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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 7, 14 p.
Morimoto, Yoshinori 1 ; Xu, Chao-Jiang 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 
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Morimoto, Yoshinori; Xu, Chao-Jiang. Regularity of weak solutions for a class of infintely degenerate elliptic semilinear equation. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2003-2004), Exposé no. 7, 14 p. http://www.numdam.org/item/SEDP_2003-2004____A7_0/

[1] J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Annales de l’École Normale Supérieure, 14 (1981), 209–246. | Numdam | Zbl

[2] M. Derridj, Un problème aux limites pour une classe d’opérateurs du second ordre hypoelliptiques, Annales de l’Institut Fourier 21 (1971), 99–148. | Numdam | Zbl

[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. | MR | Zbl

[4] H. Kumano-go, Pseudo-differential operators, MIT Press, 1982 | Zbl

[5] S. Kusuoka and D. Stroock, Applications of the Malliavin calculus, Part II, J. Fac. Sci. Univ. Tokyo Sect. IA, Math., 32, 1-76 (1985). | MR | Zbl

[6] Y. Morimoto, Hypoellipticity for infinitely degenerate elliptic operators, Osaka J. Math. 24 (1987), 13-35. | MR | Zbl

[7] Y. Morimoto, A criterion for hypoellipticity of second order differential operators, Osaka J. Math. 24 (1987), 651-675. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[10] Y. Morimoto and C.-J. Xu, Logarithmic Sobolev inequality and semi-linear Dirichlet problems for infinitely degenerate elliptic operators, Astérisque 284 (2003), 245–264. | Numdam | MR | Zbl

[11] Y. Morimoto and C.-J. Xu, Nonlinear hypoellipticity of infinite type, Preprint, 2003. | MR

[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. | MR | Zbl

[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. | MR | Zbl

[14] C.-J. Xu, Regularity problem for quasi-linear second order subelliptic equations, Comm. Pure Appl. Math., 45 77–96 (1992). | Zbl

[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. | MR | Zbl