Cet article a pour but de montrer comment, en vue de prouver certains théorèmes de régularité, des estimations classiques peuvent être remplacées par des estimations höldériennes, c’est-à-dire faisant intervenir des produits de puissances de différentes semi-normes ; ces dernières peuvent parfois être plus faciles à établir.
The aim of this paper is to show how, in order to prove regularity theorems, Hölder estimates, i.e. estimates involving products of powers of different semi-norms, can be used as well as standard estimates, and may in some instances be casier to prove.
@article{AIF_1976__26_2_35_0, author = {Unterberger, Andr\'e and Unterberger, Julianne}, title = {H\"older estimates and hypoellipticity}, journal = {Annales de l'Institut Fourier}, volume = {26}, year = {1976}, pages = {35-54}, doi = {10.5802/aif.613}, mrnumber = {54 \#5611}, zbl = {0318.35018}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1976__26_2_35_0} }
Unterberger, André; Unterberger, Julianne. Hölder estimates and hypoellipticity. Annales de l'Institut Fourier, Tome 26 (1976) pp. 35-54. doi : 10.5802/aif.613. http://gdmltest.u-ga.fr/item/AIF_1976__26_2_35_0/
[1] Spatially inhomogeneous pseudo-differential operators I, Comm. Pure Appl. Math., 27 (1974), 1-24. | MR 50 #5234 | Zbl 0279.35071
and ,[2] with the assistance of R. Vaillancourt, Pseudo-differential operators, Lecture Notes, N. Y. Univ., 1968.
,[3] Linear partial differential operators, Springer Verlag, 1963. | Zbl 0108.09301
,[4] On the singularities of solutions of partial differential equations with constant coefficients, Symp. on linear partial differential operators, Jerusalem, June 1972.
,[5] On the existence and regularity of solutions of linear pseudo-differential equations, L'Enseignement Mathématique, 17 (2) (1971), 99-163. | MR 48 #9458 | Zbl 0224.35084
,[6] Hypoelliptic second-order differential equations, Acta Math., 119 (1967), 147-171. | MR 36 #5526 | Zbl 0156.10701
,[7] Continuous dependance on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), 551-585. | MR 24 #A317 | Zbl 0097.08101
,[8] Pseudo-differential operators and hypoellipticity, Proc. Symp. Pure Math., 23 (1973), 61-69. | MR 49 #3356 | Zbl 0262.35007
,[9] Algebras of pseudo-differential operators, J. Fac. Sci. Univ. Tokyo, 17 (1970), 31-50. | MR 45 #984 | Zbl 0206.10501
,[10] Résolution d'équations aux dérivées partielles dans des espaces de distributions d'ordre de régularité variable, Ann. Inst. Fourier, 21 (1971), 85-128. | Numdam | MR 58 #29043 | Zbl 0205.43104
,[11] Ouverts stablement convexes par rapport à un opérateur différentiel, Ann. Inst. Fourier, 22 (1972), 269-290. | Numdam | MR 49 #11022 | Zbl 0228.35014
,[12] On the boundedness of pseudo-differential operators of type ρ, δ with 0 ≤ ρ ˭ δ ˂ 1, Tôhoku Math. J., 25 (1973), 339-345. | MR 49 #5948 | Zbl 0284.35068
,