-
Previous Article
The Hessian Sobolev inequality and its extensions
- DCDS Home
- This Issue
-
Next Article
Complexity and regularity of maximal energy domains for the wave equation with fixed initial data
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.
doi: 10.1215/S0012-7094-91-06408-2. |
[2] |
L. Caffarelli, The obstacle problem revisited,, J. Fourier Anal. Appl., 4 (1998), 383.
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.
doi: 10.1512/iumj.1981.30.30049. |
[4] |
D. De Silva and O. Savin, $C^\infty$ regularity of certain thin free boundaries,, submitted, (2014). Google Scholar |
[5] |
F. Ferrari, On boundary behavior of harmonic functions in Hölder domains,, J. Fourier Anal. Appl., 4 (1998), 447.
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.
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.
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.
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.
doi: 10.1215/S0012-7094-91-06408-2. |
[2] |
L. Caffarelli, The obstacle problem revisited,, J. Fourier Anal. Appl., 4 (1998), 383.
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.
doi: 10.1512/iumj.1981.30.30049. |
[4] |
D. De Silva and O. Savin, $C^\infty$ regularity of certain thin free boundaries,, submitted, (2014). Google Scholar |
[5] |
F. Ferrari, On boundary behavior of harmonic functions in Hölder domains,, J. Fourier Anal. Appl., 4 (1998), 447.
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.
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.
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.
doi: 10.1007/BF02790009. |
[1] |
Arunima Bhattacharya, Micah Warren. $ C^{2, \alpha} $ estimates for solutions to almost Linear elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021024 |
[2] |
Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure & Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261 |
[3] |
Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1757-1778. doi: 10.3934/dcdss.2020453 |
[4] |
Nikolaz Gourmelon. Generation of homoclinic tangencies by $C^1$-perturbations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 1-42. doi: 10.3934/dcds.2010.26.1 |
[5] |
Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 25-34. doi: 10.3934/dcds.2011.31.25 |
[6] |
Amit Goswami, Sushila Rathore, Jagdev Singh, Devendra Kumar. Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021021 |
[7] |
Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190 |
[8] |
Qian Liu. The lower bounds on the second-order nonlinearity of three classes of Boolean functions. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020136 |
[9] |
Sara Munday. On the derivative of the $\alpha$-Farey-Minkowski function. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 709-732. doi: 10.3934/dcds.2014.34.709 |
[10] |
Caifang Wang, Tie Zhou. The order of convergence for Landweber Scheme with $\alpha,\beta$-rule. Inverse Problems & Imaging, 2012, 6 (1) : 133-146. doi: 10.3934/ipi.2012.6.133 |
[11] |
Alexandre B. Simas, Fábio J. Valentim. $W$-Sobolev spaces: Higher order and regularity. Communications on Pure & Applied Analysis, 2015, 14 (2) : 597-607. doi: 10.3934/cpaa.2015.14.597 |
[12] |
Philippe G. Lefloch, Cristinel Mardare, Sorin Mardare. Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 341-365. doi: 10.3934/dcds.2009.23.341 |
[13] |
Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022 |
[14] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[15] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[16] |
Ka Luen Cheung, Man Chun Leung. Asymptotic behavior of positive solutions of the equation $ \Delta u + K u^{\frac{n+2}{n-2}} = 0$ in $IR^n$ and positive scalar curvature. Conference Publications, 2001, 2001 (Special) : 109-120. doi: 10.3934/proc.2001.2001.109 |
[17] |
Shihu Li, Wei Liu, Yingchao Xie. Large deviations for stochastic 3D Leray-$ \alpha $ model with fractional dissipation. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2491-2509. doi: 10.3934/cpaa.2019113 |
[18] |
Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 |
[19] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
[20] |
Hyeong-Ohk Bae, Hyoungsuk So, Yeonghun Youn. Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth. Networks & Heterogeneous Media, 2018, 13 (3) : 479-491. doi: 10.3934/nhm.2018021 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]