@article{ASENS_2007_4_40_5_765_0,
author = {Lewis, John L. and Nystr\"om, Kaj},
title = {Boundary behaviour for $p$ harmonic functions in {Lipschitz} and starlike {Lipschitz} ring domains},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {765--813},
publisher = {Elsevier},
volume = {Ser. 4, 40},
number = {5},
year = {2007},
doi = {10.1016/j.ansens.2007.09.001},
zbl = {1134.31008},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.ansens.2007.09.001/}
}
TY - JOUR AU - Lewis, John L. AU - Nyström, Kaj TI - Boundary behaviour for $p$ harmonic functions in Lipschitz and starlike Lipschitz ring domains JO - Annales scientifiques de l'École Normale Supérieure PY - 2007 SP - 765 EP - 813 VL - 40 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.ansens.2007.09.001/ DO - 10.1016/j.ansens.2007.09.001 LA - en ID - ASENS_2007_4_40_5_765_0 ER -
%0 Journal Article %A Lewis, John L. %A Nyström, Kaj %T Boundary behaviour for $p$ harmonic functions in Lipschitz and starlike Lipschitz ring domains %J Annales scientifiques de l'École Normale Supérieure %D 2007 %P 765-813 %V 40 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.ansens.2007.09.001/ %R 10.1016/j.ansens.2007.09.001 %G en %F ASENS_2007_4_40_5_765_0
Lewis, John L.; Nyström, Kaj. Boundary behaviour for $p$ harmonic functions in Lipschitz and starlike Lipschitz ring domains. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 40 (2007) no. 5, pp. 765-813. doi: 10.1016/j.ansens.2007.09.001
[1] , , Carleson type estimates for p harmonic functions and the conformal Martin boundary of John domains in metric measure spaces, Michigan Math. J. 53 (1) (2005) 165-188. | Zbl | MR
[2] Aikawa H., Kilpeläinen T., Shanmugalingam N., Zhong X., Boundary Harnack principle for p harmonic functions in smooth Euclidean domains, submitted for publication. | Zbl
[3] , , Existence and regularity for a minimum problem with free boundary, J. reine angew. Math. 325 (1981) 105-144. | Zbl | MR
[4] , Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien, Ann. Inst. Fourier (Grenoble) 28 (4) (1978) 169-213. | Zbl | MR | Numdam
[5] , , On the dimension of p harmonic measure, Ann. Acad. Sci. Fenn. 30 (2005) 459-505. | MR
[6] , , On weak reverse Hölder inequalities for nondoubling harmonic measures, Complex Variables 49 (7-9) (2004) 571-582. | Zbl
[7] , A Harnack inequality approach to the regularity of free boundaries. Part I. Lipschitz free boundaries are , Rev. Math. Iberoamericana 3 (1987) 139-162. | Zbl | MR
[8] , A Harnack inequality approach to the regularity of free boundaries. II. Flat free boundaries are Lipschitz, Comm. Pure Appl. Math. 42 (1) (1989) 55-78. | Zbl | MR
[9] , A Harnack inequality approach to the regularity of free boundaries. III. Existence theory, compactness, and dependence on X, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (4) (1989) 583-602. | MR | Numdam
[10] , , , , Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana J. Math. 30 (4) (1981) 621-640. | Zbl | MR
[11] , , Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974) 241-250. | Zbl | MR
[12] , On estimates of harmonic measure, Arch. Ration. Mech. Anal. 65 (1977) 275-288. | Zbl | MR
[13] , local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983) 827-850. | Zbl | MR
[14] , , Uniform limits of certain A-harmonic functions with applications to quasiregular mappings, Ann. Acad. Sci. Fenn. AI, Math. 16 (1991) 361-375. | Zbl | MR
[15] , , , The local regularity of solutions to degenerate elliptic equations, Comm. Partial Differential Equations 7 (1) (1982) 77-116. | Zbl | MR
[16] , , , The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (3) (1982) 151-182. | Zbl | MR | Numdam
[17] , , , Boundary behavior of solutions to degenerate elliptic equations, in: Conference on Harmonic Analysis in Honor of Antonio Zygmund, vols. I, II, Chicago, IL, 1981, Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 577-589. | Zbl | MR
[18] , On the integrability of the derivatives of a quasiconformal mapping, Acta Math. 130 (1973) 265-277. | Zbl | MR
[19] , , A regularity condition at the boundary for solutions of quasilinear elliptic equations, Arch. Ration. Mech. Anal. 67 (1977) 25-39. | Zbl | MR
[20] , , Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, 1983. | Zbl | MR
[21] , , , Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, 1993. | Zbl | MR
[22] , , The Dirichlet problem for parabolic operators with singular drift term, Mem. Amer. Math. Soc. 151 (719) (2001) 1-113. | MR
[23] , Regularity of the Poisson kernel and free boundary problems, Colloq. Math. 60-61 (1990) 547-567. | Zbl
[24] , , Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. Math. 46 (1982) 80-147. | Zbl | MR
[25] , , The logarithm of the Poisson kernel of a domain has vanishing mean oscillation, Trans. Amer. Math. Soc. 273 (1984) 781-794. | Zbl | MR
[26] , A boundary Harnack inequality for Lipschitz domains and the principle of positive singularities, Comm. Pure Appl. Math. 25 (1972) 247-255. | Zbl | MR
[27] , , Harmonic measure on locally flat domains, Duke Math. J. 87 (1997) 501-551. | Zbl | MR
[28] , , Free boundary regularity for harmonic measure and Poisson kernels, Ann. of Math. 150 (1999) 369-454. | Zbl | MR
[29] , , Poisson kernel characterization of Reifenberg flat chord arc domains, Ann. Sci. Ecole Norm. Sup. (4) 36 (3) (2003) 323-401. | Zbl | MR | Numdam
[30] Kenig C., Toro T., Free boundary regularity below the continuous threshold: 2-phase problems, submitted for publication. | Zbl
[31] , , The Dirichlet problem for elliptic operators with drift term, Publ. Mat. 45 (1) (2001) 199-217. | Zbl | MR
[32] , , Growth of entire A-subharmonic functions, Ann. Acad. Sci. Fenn. AI, Math. 28 (2003) 181-192. | Zbl | MR
[33] , On the behavior of the solutions of a quasilinear equation near null salient points of the boundary, Proc. Steklov Inst. Math. 125 (1973) 130-136. | Zbl | MR
[34] , , Uniqueness in a free boundary problem, Comm. Partial Differential Equations 31 (2006) 1591-1614. | MR
[35] Lewis J., Vogel A., Symmetry problems and uniform rectifiability, submitted for publication.
[36] , Note on p harmonic measure, Comput. Methods Funct. Theory 6 (1) (2006) 109-144. | MR
[37] , Regularity of the derivatives of solutions to certain degenerate elliptic equations, Indiana Univ. Math. J. 32 (6) (1983) 849-858. | Zbl | MR
[38] , Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12 (11) (1988) 1203-1219. | Zbl | MR
[39] , , , Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa (3) 17 (1963) 43-77. | Zbl | MR | Numdam
[40] , Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995. | Zbl | MR
[41] , Local behavior of solutions of quasilinear elliptic equations, Acta Math. 111 (1964) 247-302. | Zbl | MR
[42] , Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970. | Zbl | MR
[43] , Everywhere regularity for some quasi-linear systems with lack of ellipticity, Ann. Math. Pura Appl. 134 (4) (1984) 241-266. | Zbl | MR
[44] , Comparisons of kernel functions, boundary Harnack principle and relative Fatou theorem on Lipschitz domains, Ann. Inst. Fourier (Grenoble) 28 (4) (1978) 147-167. | Zbl | MR | Numdam
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