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Abstract: B 1 ), and uniqueness follows quickly using the maximum principle. The solution to the problem will then have a contact or coincidence set, #, where u = # and w = 0, and its complement,# , where #u = 0 and therefore #w = -##. The interface between # and# is called the free boundary. The regularity of the membrane, u, has been studied by many people, and for an obstacle, #, in C 0,# or C 1,# , u will be as smooth as #. (See [LS1], [LS2], [Fj], [BK], and [CK].) On the other hand, no... (Update)
Active bibliography (related documents): More All
4.8: Sharp Results for the Regularity and Stability of the Free.. - Blank (2001) (Correct)
1.9: Eliminating Mixed Asymptotics in Obstacle Type Free Boundary.. - Blank (Correct)
1.4: Boundary Regularity and Compactness - For Overdetermined Problems (Correct)
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BibTeX entry: (Update)
@misc{ blank-research,
author = "Ivan Blank",
title = "Research Statement",
url = "citeseer.ist.psu.edu/483939.html" }
Citations (may not include all citations):22 On extensions of the Brunn-Minkowski and Prekopa-Leindler th.. (context) - Brascamp, Lieb - 1976
6 Sharp results for the regularity and stability of the free b.. - Blank
6 Extremal eigenvalue problems for composite membranes - Cox, McLaughlin - 1990
6 the regularity of the solution of a second order variational.. (context) - Frehse - 1972
6 a regularity theorem for weak solutions to transmission prob.. (context) - Escauriaza, Fabes et al. - 1992
6 On certain problems on the maximum and minimum of characteri.. (context) - Krein - 1955
6 Solution of the Plateau Problem for m-dimensional surfaces o.. (context) - Reifenberg - 1960
6 and the convergence of coincidence sets (context) - Ca, on et al. - 1981
5 The regularity of free boundaries in higher dimensions (context) - Ca - 1977
5 The smoothness of solutions to nonlinear variational inequal.. (context) - Brezis, Kinderlehrer - 1973
4 The obstacle problem revisited (context) - Ca - 1998
3 the regularity of the solution of a variational inequality (context) - Lewy, Stampacchia - 1969
3 Potential methods in variational inequalities (context) - Ca, Kinderlehrer - 1980
3 Compactness methods in free boundary problems (context) - Ca - 1980
3 Geometric conditions and existence of bi-Lipschitz parameter.. (context) - Toro - 1995
3 Harmonic measures and Poisson Kernels (context) - Kenig, Toro
2 Gradient estimates for solutions to divergence form elliptic.. (context) - Li, Vogelius - 2000
2 the smoothness of superharmonics which solve a minimum probl.. (context) - Lewy, Stampacchia - 1970
2 Harmonic measure on locally flat domains (context) - Kenig, Toro - 1997
2 An elliptic regularity result for a composite medium with (context) - Bonnetier, Vogelius - 2000
2 Symmetry breaking and other phenomena in the optimization of.. (context) - Chanillo, Grieser et al. - 2000
2 Doubling and flatness: geometry of measures (context) - Toro - 1997
2 The free boundary problem in the optimization of composite m.. (context) - Chanillo, Grieser et al.
2 Obstacle problem for nonlinear 2 nd -order elliptic operator - Lee
1 estimates for elliptic equations in divergence form (context) - Ca, Peral - 1998
1 Free boundary problems for parabolic equations (context) - Friedman - 1960
1 Course notes of Y (context) - Li, Nirenberg
Documents on the same site (http://www.math.rutgers.edu/~blanki): More
Sharp Results for the Regularity and Stability of the Free.. - Blank (2001) (Correct)
Boundary Regularity and Compactness - For Overdetermined Problems (Correct)
Eliminating Mixed Asymptotics in Obstacle Type Free Boundary.. - Blank (Correct)
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