Harmonic spaces associated with adjoints of linear elliptic operators

Peter Sjögren

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 3-4, page 509-518
  • ISSN: 0373-0956

Abstract

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Let L be an elliptic linear operator in a domain in R n . We imposse only weak regularity conditions on the coefficients. Then the adjoint L * exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type L * u = given distribution. We then apply to L * R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of L * are also studied. The results generalize earlier work of the author.

How to cite

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Sjögren, Peter. "Harmonic spaces associated with adjoints of linear elliptic operators." Annales de l'institut Fourier 25.3-4 (1975): 509-518. <http://eudml.org/doc/74259>.

@article{Sjögren1975,
abstract = {Let $L$ be an elliptic linear operator in a domain in $\{\bf R\}^n$. We imposse only weak regularity conditions on the coefficients. Then the adjoint $L^*$ exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type $L^* u = $ given distribution. We then apply to $L^*$ R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of $L^*$ are also studied. The results generalize earlier work of the author.},
author = {Sjögren, Peter},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3-4},
pages = {509-518},
publisher = {Association des Annales de l'Institut Fourier},
title = {Harmonic spaces associated with adjoints of linear elliptic operators},
url = {http://eudml.org/doc/74259},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Sjögren, Peter
TI - Harmonic spaces associated with adjoints of linear elliptic operators
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 3-4
SP - 509
EP - 518
AB - Let $L$ be an elliptic linear operator in a domain in ${\bf R}^n$. We imposse only weak regularity conditions on the coefficients. Then the adjoint $L^*$ exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type $L^* u = $ given distribution. We then apply to $L^*$ R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of $L^*$ are also studied. The results generalize earlier work of the author.
LA - eng
UR - http://eudml.org/doc/74259
ER -

References

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  1. [1] S. AGMON, A. DOUGLIS and L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I., Comm. Pure Appl. Math., 12 (1959), 623-727. Zbl0093.10401MR23 #A2610
  2. [2] N. BOBOC and P. MUSTATA, Espaces harmoniques associés aux opérateurs différentiels linéaires du second ordre de type elliptique, Lectures Notes in Mathematics, 68, Springer-Verlag, Berlin 1968. Zbl0167.40301MR39 #3020
  3. [3] J.-M. BONY, Principe du maximum dans les espaces de Sobolev, C. R. Acad. Sc., Paris, 265 (1967), 333-336. Zbl0164.16803MR36 #6759
  4. [4] F. E. BROWDER, Functional analysis and partial différential equations II, Math. Ann., 145 (1962), 81-226. Zbl0103.31602MR25 #318
  5. [5] R.-M. HERVÉ, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. Zbl0101.08103MR25 #3186
  6. [6] C. MIRANDA, Partial Differential Equations of Elliptic Type, Second Revised Edition. Springer-Verlag, Berlin 1970. Zbl0198.14101MR44 #1924
  7. [7] P. SJÖGREN, On the adjoint of an elliptic linear differential operator and its potential theory, Ark. Mat., 11 (1973), 153-165. Zbl0267.31011MR49 #10899

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