Ancona, Alano Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien. (French) Zbl 0377.31001 Ann. Inst. Fourier 28, No. 4, 169-213 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 80 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [1] , Remarques sur la variation des fonctions harmoniques et les masses associées. Application, Ann. Inst. Fourier, II (1950), 101-111. · Zbl 0042.33604 [2] [1bis] , Sur le principe des singularités positives et la topologie de R.S. Martin, Ann. Univ. Grenoble, 23, 298-30 (1950), 307. [3] [2] et , Espaces harmoniques associés aux opérateurs différentiels linéaires du second ordre de type elliptique, Lecture Notes, 68, Springer Verlag (1968). · Zbl 0167.40301 [4] [3] , On the existence of boundary values for harmonic functions of several variables, Ark. Math., 4 (1962). · Zbl 0107.08402 [5] [4] , A note on sets of harmonic measure zero, Preprint. [6] [5] et , On isolated singularities of solutions of second order elliptic equations, J. d’Anal. Math., 4 (1954-1956), 309-340. · Zbl 0071.09701 [7] [6] , Fatou-Doob limit theorems in the axiomatic system of Brelot, Ann. Inst. Fourier, 16 (1966), 455-467. · Zbl 0145.15103 [8] [7] , Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415-571. · Zbl 0101.08103 [9] [8] , Uber die existenz harmonisher minoranten von superharmonishen Funktionen, Mat. Ann., 225 (1977), 99-114. · Zbl 0319.31008 [10] [9] , 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] [10] and , On the boundary values of harmonic functions, Trans. Amer. Math. Soc., 132, n° 2 (1968), 307-322. · Zbl 0159.40501 [12] [11] and , Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc., 147 (1970), 507-527. · Zbl 0193.39601 [13] [12] , Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172. · JFM 67.0343.03 [14] [13] , Barriers on cones for uniformly elliptic operators, Ann. Math. pura ed. applicata, IV, vol. 76 (1967), 93-106. · Zbl 0149.32101 [15] [14] , Partial differential equations of elliptic type, Springer Verlag (1970). · Zbl 0198.14101 [16] [15] , On the Martin compactification of a bounded Lipschitz domain in a Riemannian manifold, Preprint. · Zbl 0363.31010 [17] [16] , On the Harnack inequality for linear elliptic equations, J. d’Anal. Math., 4 (1956), 292-308. · Zbl 0070.32302 [18] [17] , 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] [18] , Inequalities for the Green function and boundary of the gradient of solutions of elliptic equations, Math. Scand., 21 (1967), 17-37. · Zbl 0164.13101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.