Identifiability at the boundary for first-order terms

References

• Alessandrini , G . 1990 . Singular solutions of elliptic equations and the determination of conductivity byboundarymeasurements . Journal of Differential Equations , 84 : 252 – 272 .
   Web of Science ®Google Scholar
• Brown , RM . 2001 . Recovering the conductivity at the boundary from the Dirichlet to Neumann map: apointwiseresult . Journal of Inverse Ill-Posed Problems , 9 ( 6 ) : 567 – 574 .
   Google Scholar
• Cheng , J , Nakamura , G and Somersalo , E . 2001 . Uniqueness of identifying the convection term . KoreanMathematical Society, Communications , 16 ( 3 ) : 405 – 413 . Second Japan-Korea Joint Seminar onInverse Problems andRelated Topics (Seoul, 2001)
   Google Scholar
• Cheng , J and Yamamoto , M . 2004 . Determination of two convection coefficients from Dirichlet toNeumann map in the two-dimensional case . SIAM Journal of Mathematical Analysis , 35 ( 6 ) : 1371 – 1393 . (electronic)
   Web of Science ®Google Scholar
• Eskin , G and Ralston , J . 1995 . Inverse scattering problem for the Schrödinger equation with magnetic potentialat a fixed energy . Communications in Mathematical Physics , 173 ( 1 ) : 199 – 224 .
   Web of Science ®Google Scholar
• Gilbarg , D and Trudinger , NS . 1983 . Elliptic Partial Differential Equations of Second Order , Berlin : Springer-Verlag .
   Google Scholar
• Isakov , V . 2001 . Uniqueness of recovery of some quasilinear partial differential equations . Communications in Partial Differential Equations , 26 ( 11–12 ) : 1947 – 1973 .
   Web of Science ®Google Scholar
• Jerison , DS and Kenig , CE . 1982 . “ Boundary value problems in Lipschitz domains. In:WalterLittman(Ed.) ” . In Studies in Partial Differential Equations , volumeume23 , 1 – 68 . Washington, DC : Math. Assoc. Amer . of MAA Studies in Mathematics
   Google Scholar
• Kang , H and Yun , K . 2002 . Boundary determination of conductivities and Riemannian metrics via local Dirichlet-to-Neumann operator . SIAM Journal of Mathematical Analysis , 34 ( 3 ) : 719 – 735 . (electronic)
   Web of Science ®Google Scholar
• Nakamura , G and Sun, Z.and Uhlmann , G . 1995 . Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field . Mathematische Annalen , 303 ( 3 ) : 377 – 388 .
   Web of Science ®Google Scholar
• Nakamura , G and Tanuma , K . 2001 . Local determination of conductivity at the boundary from the Dirichlet-to-Neumann map . Inverse Problems , 17 ( 3 ) : 405 – 419 .
   Web of Science ®Google Scholar
• Salo , M . 2004 . Inverse problems for non-smooth first order perturbations of the Laplacian . AnnalesAcademiae Scientiarum Fennicae, Annales, Mathematica,Dissertationes , : 139
   Google Scholar
• Sun , Z . 1993 . An inverse boundary value problem for Schrödinger operators with vector potentials . Transactions of the American Mathematical Society , 338 : 953 – 969 .
   Web of Science ®Google Scholar
• Tamasan , A . 2004 . On the scattering method for the ∂-equation and reconstruction of convection coefficients . Inverse Problems , 20 ( 6 ) : 1807 – 1817 .
   Web of Science ®Google Scholar
• Tolmasky , CF . 1998 . Exponentially growing solutions for nonsmooth first-order perturbations of the Laplacian . SIAM Journal of Mathematical Analysis , 29 ( 1 ) : 116 – 133 . (electronic)
   Web of Science ®Google Scholar
• Tong , CL and Cheng , J.and Yamamoto, M. 2005 . Reconstruction of convection coefficients of an elliptic equationin the plane by Dirichlet to Neumann mapping . Sci. China Ser. A, , 48 : 40 – 56 .
   Google Scholar
• Widman , KO . 1967 . Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations . Mathematica Scandinavica , 21 : 17 – 37 .
   Web of Science ®Google Scholar