References
- Vogelius , M and Xu , J-M . 1998 . A nonlinear elliptic boundary value problem related to corrosion modeling . Quarterly of Applied Mathematics , 56 : 479 – 505 .
- Bryan , K and Vogelius , M . 2002 . Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling . Quarterly of Applied Mathematics , 60 : 675 – 694 .
- Kavian , O and Vogelius , M . 2003 . On the existence and “blow-up” of solutions of a two dimensional nonlinear boundary value problem arising in corrosion modeling . Proceedings of the Royal Society of Edinburgh , 133A : 119 – 149 .
- Medville , K and Vogelius , M . Blow up behaviour of planar harmonic functions satisfying a certain exponential Neumann boundary condition . SIAM Journal on Mathematical Analysis , 36 ( 6 ) 1772 – 1806 .
- Fasino , D and Inglese , G . 1999 . An inverse Robin problem for Laplaces equation: theoretical results and numerical methods . Inverse Problems , 15 : 41 – 48 .
- Alessandrini , G , Del Piero , L and Rondi , L . 2003 . Stable determination of corrosion by a single electrostatic boundary measurement . Inverse Problems , 19 ( 4 ) : 973 – 984 .
- Chaabane , S , Fellah , I , Jaoua , M and Leblond , J . 2004 . Logarithmic stability estimates for a Robin coefficient in two-dimensional Laplace inverse problems . Inverse Problems , 20 ( 1 ) : 47 – 59 .
- Cannon , JR . 1967 . Determination of the unknown coefficient k(u) in the equation ∇ k(u)∇ u=0 from overspecified boundary data . Journal of Mathematical Analysis and Applications , 18 : 112 – 114 .
- Beretta , E and Vogelius , M . 1991 . An inverse problem originating from magnetohydrodynamics . Archive for Rational Mechanics and Analysis , 115 ( 2 ) : 137 – 152 .
- Isakov , V and Sylvester , J . 1994 . Global uniqueness for a semilinear elliptic inverse problem . Communications on Pure and Applied Mathematics , 47 : 1403 – 1410 .
- Sun , Z . 1996 . On a quasilinear inverse boundary problem . Mathematische Zeitschrift , 221 : 293 – 305 .
- Isakov , V . 1990 . “ Inverse source problems ” . In Mathematical surveys and monographs , Vol. 34 , Providence, , USA : AMS .
- Trytten , GN . 1963 . Pointwise bound for solution of the Cauchy problem for elliptic equations . Archive for Rational Mechanics and Analysis , 13 : 22 – 224 .
- Payne , LE . 1970 . On a priori bounds in the Cauchy problem for elliptic equations . SIAM Journal on Mathematical Analysis , 1 : 82 – 89 .
- Agmon , S , Douglis , A and Nirenberg , L . 1959 . Estimates near the boundary for solution of elliptic partial differential equations satisfying general boundary conditions. I . Communications on Pure and Applied Mathematics , 12 : 623 – 727 .
- Alessandrini , G , Beretta , E , Rosset , E and Vessella , S . 2000 . Optimal stability for inverse elliptic boundary value problems with unknown boundaries . Annali della Scuola Normale Superiore di Pisa Classe di Scienze , 29 ( 4 ) : 755 – 806 .
- Adams , RA . 1975 . Sobolev Spaces , New York, San Francisco, London : Academic Press .
- Gilbarg , D and Trudinger , NS . 1977 . Elliptic Partial Differential Equations of Second Order, , 2nd Edn , Berlin, Heidelberg, New York : Springer-Verlag .
- Lieberman , GM . 1985 . Regularized distance and its applications . Pacific Journal of Mathematics , 117 : 329 – 353 .
- Korevaar , J and Meyers , JLH . 1994 . Logarithmic convexity for supremum norms of harmonic functions . The Bulletin of the London Mathematical Society , 26 : 353 – 362 .
- Alessandrini , G and DiBenedetto , E . 1997 . Determining 2-dimensional cracks in 3-dimensional bodies: uniqueness and stability . Indiana University Mathematics Journal , 46 ( 1 ) : 1 – 82 .