Hölder estimates and hypoellipticity

André Unterberger; Julianne Unterberger

Annales de l'institut Fourier (1976)

  • Volume: 26, Issue: 2, page 35-54
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Unterberger, André, and Unterberger, Julianne. "Hölder estimates and hypoellipticity." Annales de l'institut Fourier 26.2 (1976): 35-54. <http://eudml.org/doc/74284>.

@article{Unterberger1976,
abstract = {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.},
author = {Unterberger, André, Unterberger, Julianne},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {35-54},
publisher = {Association des Annales de l'Institut Fourier},
title = {Hölder estimates and hypoellipticity},
url = {http://eudml.org/doc/74284},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Unterberger, André
AU - Unterberger, Julianne
TI - Hölder estimates and hypoellipticity
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 2
SP - 35
EP - 54
AB - 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.
LA - eng
UR - http://eudml.org/doc/74284
ER -

References

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  1. [1] R. BEALS and C. FEFFERMAN, Spatially inhomogeneous pseudo-differential operators I, Comm. Pure Appl. Math., 27 (1974), 1-24. Zbl0279.35071MR50 #5234
  2. [2] K. O. FRIEDRICHS, with the assistance of R. Vaillancourt, Pseudo-differential operators, Lecture Notes, N. Y. Univ., 1968. 
  3. [3] L. HÖRMANDER, Linear partial differential operators, Springer Verlag, 1963. Zbl0108.09301
  4. [4] L. HÖRMANDER, On the singularities of solutions of partial differential equations with constant coefficients, Symp. on linear partial differential operators, Jerusalem, June 1972. Zbl0247.35005
  5. [5] L. HÖRMANDER, On the existence and regularity of solutions of linear pseudo-differential equations, L'Enseignement Mathématique, 17 (2) (1971), 99-163. Zbl0224.35084MR48 #9458
  6. [6] L. HÖRMANDER, Hypoelliptic second-order differential equations, Acta Math., 119 (1967), 147-171. Zbl0156.10701MR36 #5526
  7. [7] F. JOHN, Continuous dependance on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math., 13 (1960), 551-585. Zbl0097.08101MR24 #A317
  8. [8] J. KOHN, Pseudo-differential operators and hypoellipticity, Proc. Symp. Pure Math., 23 (1973), 61-69. Zbl0262.35007MR49 #3356
  9. [9] H. KUMANO-GO, Algebras of pseudo-differential operators, J. Fac. Sci. Univ. Tokyo, 17 (1970), 31-50. Zbl0206.10501MR45 #984
  10. [10] A. UNTERBERGER, Résolution d'équations aux dérivées partielles dans des espaces de distributions d'ordre de régularité variable, Ann. Inst. Fourier, 21 (1971), 85-128. Zbl0205.43104MR58 #29043
  11. [11] A. UNTERBERGER, Ouverts stablement convexes par rapport à un opérateur différentiel, Ann. Inst. Fourier, 22 (1972), 269-290. Zbl0228.35014MR49 #11022
  12. [12] K. WATANABE, On the boundedness of pseudo-differential operators of type ρ, δ with 0 ≤ ρ ˭ δ ˂ 1, Tôhoku Math. J., 25 (1973), 339-345. Zbl0284.35068MR49 #5948

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