# Harmonic spaces associated with adjoints of linear elliptic operators

Annales de l'institut Fourier (1975)

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

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topSjögren, 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

top- [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] 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] J.-M. BONY, Principe du maximum dans les espaces de Sobolev, C. R. Acad. Sc., Paris, 265 (1967), 333-336. Zbl0164.16803MR36 #6759
- [4] F. E. BROWDER, Functional analysis and partial différential equations II, Math. Ann., 145 (1962), 81-226. Zbl0103.31602MR25 #318
- [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] C. MIRANDA, Partial Differential Equations of Elliptic Type, Second Revised Edition. Springer-Verlag, Berlin 1970. Zbl0198.14101MR44 #1924
- [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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