On the Two-Phase Membrane Problem With Coefficients Below the Lipschitz Threshold
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2359-2372.
@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},
     pages = {2359--2372},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.03.006},
     mrnumber = {2569898},
     zbl = {1180.35194},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.03.006/}
}
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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) no. 6, pp. 2359-2372. doi : 10.1016/j.anihpc.2009.03.006. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.03.006/

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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