This is a preview of subscription content, log in via an institution to check access.
References
Beals, R. andFefferman, C., On local solvability of linear partial differential equations,Ann. of Math. 97 (1973), 482–498.
Dencker, N., On the propagation of singularities for pseudo-differential operators of principal type,Ark. Mat. 20 (1982), 23–60.
Dencker, N., The solvability of nonL 2 solvable operators,Journees “Équations aux Dérivées Partielles”, École Polytechnique, Centre de Mathématiques, Palaiseau, 1996.
Dencker, N., A class of solvable operators, inGeometrical Optics and Related Topics (Colombini, F. and Lerner, N., eds.), pp. 141–177, Birkhäuser, Boston, Mass., 1997.
Dencker, N., A new type of estimate for operators on Hilbert spaces, Preprint, 1997.
Dencker, N., A sufficient condition for solvability, to appear inInternat. Math. Res. Notices.
Dencker, N., Morimoto, Y. andMorioka, T., Hypoellipticity for operators of infinitely degenerate Egorov type, to appear inTsukuba J. Math.
Egorov, Yu. V., Subelliptic operators,Uspekhi Mat. Nauk 30:3 (1975), 57–104. (Russian). English transl.:Russian Math. Surveys 30:3 (1975), 55–105.
Hörmander, L.,The Analysis of Linear Partial Differential Operators, vol.I-IV, Springer-Verlag, Berlin-Heidelberg, 1983–1985.
Hörmander, L., On the solvability of pseudodifferential equations, inStructure of Solutions of Differential Equations (Morimoto, M. and Kawai, T., eds.), pp. 183–213, World Scientific, River Edge, N. J., 1996.
Lerner, N., Sufficiency of condition (Ψ) for local solvability in two dimensions,Ann. of Math. 128 (1988), 243–258.
Lerner, N., Nonsolvability inL 2 for a first order operator satisfying condition (Ψ),Ann. of Math. 139 (1994), 363–393.
Lerner, N., Energy methods via coherent states and advanced pseudo-differential calculus, inMultidimensional Complex Analysis and Partial Differential Equations (Cordaro, P. D., Jacobowitz H. and Gidikin, S., eds.), Contemp. Math.205, pp. 177–201, Amer. Math. Soc., Providence, R. I., 1997).
Lerner, N., Perturbation and energy estimates,Ann. Sci. École Norm. Sup. 31 (1998), 843–886.
Lerner, N., Factorization and solvability, Preprint, 1997.
Menikoff, A., On local solvability of pseudo-differential equations,Proc. Amer. Math. Soc. 43 (1974), 149–154.
Morimoto, Y., Hypoelliptic operators of principal type with infinite degeneracy,Tsukuba J. Math. 19 (1995), 187–200.
Morimoto, Y., Local solvability and hypoellipticity for pseudodifferential operators of Egorov type with infinite degeneracy,Nagoya Math. J. 139 (1995), 151–171.
Nirenberg, L. andTreves, F., On local solvability of linear partial differential equations. Part I: Necessary conditions,Comm. Pure Appl. Math. 23 (1970), 1–38; Part II: Sufficient conditions,Comm. Pure Appl. Math. 23 (1970), 459–509; Correction,Comm. Pure Appl. Math. 24 (1971), 279–288.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dencker, N. Estimates and solvability. Ark. Mat. 37, 221–243 (1999). https://doi.org/10.1007/BF02412212
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02412212