On the two-phase membrane problem with coefficients below the Lipschitz threshold
Erik Lindgren; Henrik Shahgholian; Anders Edquist
Annales de l'I.H.P. Analyse non linéaire (2009)
- Volume: 26, Issue: 6, page 2359-2372
- ISSN: 0294-1449
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topLindgren, Erik, Shahgholian, Henrik, and Edquist, Anders. "On the two-phase membrane problem with coefficients below the Lipschitz threshold." Annales de l'I.H.P. Analyse non linéaire 26.6 (2009): 2359-2372. <http://eudml.org/doc/78937>.
@article{Lindgren2009,
author = {Lindgren, Erik, Shahgholian, Henrik, Edquist, Anders},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {obstacle problem; elliptic equation; regularity; free boundary},
language = {eng},
number = {6},
pages = {2359-2372},
publisher = {Elsevier},
title = {On the two-phase membrane problem with coefficients below the Lipschitz threshold},
url = {http://eudml.org/doc/78937},
volume = {26},
year = {2009},
}
TY - JOUR
AU - Lindgren, Erik
AU - Shahgholian, Henrik
AU - Edquist, Anders
TI - On the two-phase membrane problem with coefficients below the Lipschitz threshold
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 6
SP - 2359
EP - 2372
LA - eng
KW - obstacle problem; elliptic equation; regularity; free boundary
UR - http://eudml.org/doc/78937
ER -
References
top- [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. Zbl0844.35137MR732100
- [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. Zbl0123.28706MR162050
- [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. Zbl1032.35170MR1871348
- [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. Zbl1170.35484MR2040643
- [5] Caffarelli L.A., The obstacle problem revisited, J. Fourier Anal. Appl.4 (4–5) (1998) 383-402. Zbl0928.49030MR1658612
- [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. Zbl1142.35382MR1906591
- [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. Zbl1031.28004MR1808649
- [8] Edquist Anders, Lindgren Erik, A two-phase obstacle-type problem for the p-laplacian, Calc. Var. Partial Differential Equations35 (4) (2009) 421-433. Zbl1177.35259MR2496650
- [9] Kinderlehrer D., Nirenberg L., Spruck J., Regularity in elliptic free boundary problems, J. Anal. Math.34 (1978/1979) 86-119. Zbl0402.35045MR531272
- [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. Zbl0457.35001MR567696
- [11] Reifenberg E.R., Solution of the Plateau problem for m-dimensional surfaces of varying topological type, Acta Math.104 (1960) 1-92. Zbl0099.08503MR114145
- [12] Shahgholian Henrik, regularity in semilinear elliptic problems, Comm. Pure Appl. Math.56 (2) (2003) 278-281. Zbl1258.35098MR1934623
- [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. Zbl1057.35098MR2065019
- [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. IMRN8 (2007), Art. ID rnm026, 16 pp. Zbl1175.35157MR2340105
- [15] Uraltseva N.N., Two-phase obstacle problem, Function theory and phase transitions, J. Math. Sci. (N. Y.)106 (3) (2001) 3073-3077. MR1906034
- [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. Zbl0986.35139MR1825655
- [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. Zbl0164.13101MR239264
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