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Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien. (French) Zbl 0377.31001


MSC:

31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
35J15 Second-order elliptic equations
47F05 General theory of partial differential operators
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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References:

[1] M. BRELOT, Remarques sur la variation des fonctions harmoniques et LES masses associées. Application, Ann. Inst. Fourier, II (1950), 101-111. · Zbl 0042.33604
[2] M. BRELOT, Sur le principe des singularités positives et la topologie de R.S. martin, Ann. Univ. Grenoble, 23, 298-30 (1950), 307.
[3] N. BOBOC et P. MUSTATA, Espaces harmoniques associés aux opérateurs différentiels linéaires du second ordre de type elliptique, Lecture Notes, 68, Springer Verlag (1968). · Zbl 0167.40301
[4] L. CARLESON, On the existence of boundary values for harmonic functions of several variables, Ark. Math., 4 (1962). · Zbl 0107.08402
[5] B. DAHLBERG, A note on sets of harmonic measure zero, Preprint.
[6] D. GILDBARG et J. SERRIN, On isolated singularities of solutions of second order elliptic equations, J. d’Anal. Math., 4 (1954-1956), 309-340. · Zbl 0071.09701
[7] K. GOWRISANKARAN, Fatou-Doob limit theorems in the axiomatic system of Brelot, Ann. Inst. Fourier, 16 (1966), 455-467. · Zbl 0145.15103
[8] R. M. HERVÉ, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. · Zbl 0101.08103
[9] H. HUEBER, Uber die existenz harmonisher minoranten von superharmonishen funktionen, Mat. Ann., 225 (1977), 99-114. · Zbl 0319.31008
[10] J. T. KEMPER, A boundary Harnack principle for Lipschitz domains and the principle of positive singularities, Comm. pure appl. math., 25 (1972), 247-255. · Zbl 0226.31007
[11] R. A. HUNT and R. L. WHEEDEN, On the boundary values of harmonic functions, Trans. Amer. Math. Soc., 132, n° 2 (1968), 307-322. · Zbl 0159.40501
[12] R. A. HUNT and R. L. WHEEDEN, Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc., 147 (1970), 507-527. · Zbl 0193.39601
[13] R. S. MARTIN, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172. · JFM 67.0343.03
[14] K. MILLER, Barriers on cones for uniformly elliptic operators, Ann. Math. pura ed. applicata, IV, vol. 76 (1967), 93-106. · Zbl 0149.32101
[15] C. MIRANDA, Partial differential equations of elliptic type, Springer Verlag (1970). · Zbl 0198.14101
[16] J. C. TAYLOR, On the martin compactification of a bounded Lipschitz domain in a Riemannian manifold, Preprint. · Zbl 0363.31010
[17] J. SERRIN, On the Harnack inequality for linear elliptic equations, J. d’Anal. Math., 4 (1956), 292-308. · Zbl 0070.32302
[18] C. DE LA VALLÉE POUSSIN, Propriétés des fonctions harmoniques dans un domaine limité par des surfaces à courbure bornée, Ann. Scuola Norm. Sup. di Pisa, 2, vol 2 (1933), 167-192. · JFM 59.1136.02
[19] K. O. WIDMANN, Inequalities for the Green function and boundary of the gradient of solutions of elliptic equations, Math. Scand., 21 (1967), 17-37. · Zbl 0164.13101
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