On the Two-Phase Membrane Problem With Coefficients Below the Lipschitz Threshold
Lindgren, Erik ; Shahgholian, Henrik ; Edquist, Anders
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 2359-2372 / Harvested from Numdam
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@article{AIHPC_2009__26_6_2359_0,
     author = {Lindgren, Erik and Shahgholian, Henrik and Edquist, Anders},
     title = {On the Two-Phase Membrane Problem With Coefficients Below the Lipschitz Threshold},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {2359-2372},
     doi = {10.1016/j.anihpc.2009.03.006},
     mrnumber = {2569898},
     zbl = {1180.35194},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2359_0}
}

Lindgren, Erik; Shahgholian, Henrik; Edquist, Anders. On the Two-Phase Membrane Problem With Coefficients Below the Lipschitz Threshold. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2359-2372. doi : 10.1016/j.anihpc.2009.03.006. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2359_0/

[1] Alt Hans Wilhelm, Caffarelli Luis A., Friedman Avner, Variational Problems With Two Phases and Their Free Boundaries, Trans. Amer. Math. Soc. 282 (2) (1984) 431-461. | MR 732100 | Zbl 0844.35137

[2] Agmon S., Douglis A., Nirenberg L., Estimates Near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions. II, Comm. Pure Appl. Math. 17 (1964) 35-92. | MR 162050 | Zbl 0123.28706

[3] Blank Ivan, Sharp Results for the Regularity and Stability of the Free Boundary in the Obstacle Problem, Indiana Univ. Math. J. 50 (3) (2001) 1077-1112. | MR 1871348 | Zbl 1032.35170

[4] Blank Ivan, Shahgholian Henrik, Boundary Regularity and Compactness for Overdetermined Problems, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (4) (2003) 787-802. | Numdam | MR 2040643 | Zbl 1170.35484

[5] Caffarelli L. A., The Obstacle Problem Revisited, J. Fourier Anal. Appl. 4 (4-5) (1998) 383-402. | MR 1658612 | Zbl 0928.49030

[6] Caffarelli Luis A., Jerison David, Kenig Carlos E., Some New Monotonicity Theorems With Applications to Free Boundary Problems, Ann. of Math. (2) 155 (2) (2002) 369-404. | MR 1906591 | Zbl 1142.35382

[7] David Guy, Kenig Carlos, Toro Tatiana, Asymptotically Optimally Doubling Measures and Reifenberg Flat Sets With Vanishing Constant, Comm. Pure Appl. Math. 54 (4) (2001) 385-449. | MR 1808649 | Zbl 1031.28004

[8] Edquist Anders, Lindgren Erik, A Two-Phase Obstacle-Type Problem for the P-Laplacian, Calc. Var. Partial Differential Equations 35 (4) (2009) 421-433. | MR 2496650 | Zbl 1177.35259

[9] Kinderlehrer D., Nirenberg L., Spruck J., Regularity in Elliptic Free Boundary Problems, J. Anal. Math. 34 (1978/1979) 86-119. | MR 531272 | Zbl 0402.35045

[10] Kinderlehrer David, Stampacchia Guido, An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math., vol. 88, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1980. | MR 567696 | Zbl 0457.35001

[11] Reifenberg E. R., Solution of the Plateau Problem for M-Dimensional Surfaces of Varying Topological Type, Acta Math. 104 (1960) 1-92. | MR 114145 | Zbl 0099.08503

[12] Shahgholian Henrik, C 1,1 Regularity in Semilinear Elliptic Problems, Comm. Pure Appl. Math. 56 (2) (2003) 278-281. | MR 1934623 | Zbl pre01860597

[13] Shahgholian Henrik, Uraltseva Nina, Weiss Georg S., Global Solutions of an Obstacle-Problem-Like Equation With Two Phases, Monatsh. Math. 142 (1-2) (2004) 27-34. | MR 2065019 | Zbl 1057.35098

[14] Shahgholian Henrik, Uraltseva Nina, Weiss Georg S., The Two-Phase Membrane Problem-Regularity of the Free Boundaries in Higher Dimensions, Int. Math. Res. Not. IMRN 8 (2007), Art. ID rnm026, 16 pp. | MR 2340105 | Zbl 1175.35157

[15] Uraltseva N. N., Two-Phase Obstacle Problem, Function theory and phase transitions, J. Math. Sci. (N. Y.) 106 (3) (2001) 3073-3077. | MR 1906034

[16] Weiss G. S., An Obstacle-Problem-Like Equation With Two Phases: Pointwise Regularity of the Solution and an Estimate of the Hausdorff Dimension of the Free Boundary, Interfaces Free Bound. 3 (2) (2001) 121-128. | MR 1825655 | Zbl 0986.35139

[17] Widman Kjell-Ove, Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations, Math. Scand. 21 (1967/1968) 17-37. | MR 239264 | Zbl 0164.13101