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A note on higher regularity boundary Harnack inequality
| 1. | Department of Mathematics, Barnard College, Columbia University, 2990 Broadway, New York, NY 10027, United States |
| 2. | Department of Mathematics, Columbia University, New York, NY 10027, United States |
References:
| [1] |
R. Bañuelos, R. F. Bass and K. Burdzy, Hölder domains and the boundary Harnack principle, Duke Math. J., 64 (1991), 195-200.
doi: 10.1215/S0012-7094-91-06408-2. |
| [2] |
L. Caffarelli, The obstacle problem revisited, J. Fourier Anal. Appl., 4 (1998), 383-402.
doi: 10.1007/BF02498216. |
| [3] |
L. Caffarelli, E. Fabes, S. Mortola and S. Salsa, Boundary behavior of non-negative solutions of elliptic operators in divergence form, Indiana Math. J., 30 (1981), 621-640.
doi: 10.1512/iumj.1981.30.30049. |
| [4] |
D. De Silva and O. Savin, $C^\infty$ regularity of certain thin free boundaries, submitted, arXiv:1402.1098, 2014. |
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F. Ferrari, On boundary behavior of harmonic functions in Hölder domains, J. Fourier Anal. Appl., 4 (1998), 447-461.
doi: 10.1007/BF02498219. |
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R. A. Hunt and R. L. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc., 132 (1968), 307-322.
doi: 10.1090/S0002-9947-1968-0226044-7. |
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D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. Math., 46 (1982), 80-147.
doi: 10.1016/0001-8708(82)90055-X. |
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D. Kinderlehrer, L. Nirenberg and J. Spruck, Regularity in elliptic free boundary problems, J. Analyse Math., 34 (1978), 86-119 (1979).
doi: 10.1007/BF02790009. |
show all references
References:
| [1] |
R. Bañuelos, R. F. Bass and K. Burdzy, Hölder domains and the boundary Harnack principle, Duke Math. J., 64 (1991), 195-200.
doi: 10.1215/S0012-7094-91-06408-2. |
| [2] |
L. Caffarelli, The obstacle problem revisited, J. Fourier Anal. Appl., 4 (1998), 383-402.
doi: 10.1007/BF02498216. |
| [3] |
L. Caffarelli, E. Fabes, S. Mortola and S. Salsa, Boundary behavior of non-negative solutions of elliptic operators in divergence form, Indiana Math. J., 30 (1981), 621-640.
doi: 10.1512/iumj.1981.30.30049. |
| [4] |
D. De Silva and O. Savin, $C^\infty$ regularity of certain thin free boundaries, submitted, arXiv:1402.1098, 2014. |
| [5] |
F. Ferrari, On boundary behavior of harmonic functions in Hölder domains, J. Fourier Anal. Appl., 4 (1998), 447-461.
doi: 10.1007/BF02498219. |
| [6] |
R. A. Hunt and R. L. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc., 132 (1968), 307-322.
doi: 10.1090/S0002-9947-1968-0226044-7. |
| [7] |
D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in non-tangentially accessible domains, Adv. Math., 46 (1982), 80-147.
doi: 10.1016/0001-8708(82)90055-X. |
| [8] |
D. Kinderlehrer, L. Nirenberg and J. Spruck, Regularity in elliptic free boundary problems, J. Analyse Math., 34 (1978), 86-119 (1979).
doi: 10.1007/BF02790009. |
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