Energy and regularity dependent stability estimates for the Gel’fand inverse problem in multidimensions
نویسنده
چکیده
We prove new global Hölder-logarithmic stability estimates for the Gel’fand inverse problem at fixed energy in dimension d ≥ 3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. Comparisons with preceeding results in this direction are given.
منابع مشابه
Energy and regularity dependent stability estimates for near-field inverse scattering in multidimensions
We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimension d ≥ 3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension d = 2 is also gi...
متن کاملEffectivized Holder-logarithmic stability estimates for the Gel'fand inverse problem
We give effectivized Hölder-logarithmic energy and regularity dependent stability estimates for the Gel’fand inverse boundary value problem in dimension d = 3. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in L and L∞ norms for the coefficient difference and related stability efficiently increases with...
متن کاملOn stability estimates in the Gel’fand-Calderon inverse problem
We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D.
متن کاملInstability in the Gel’fand inverse problem at high energies
We give an instability estimate for the Gel’fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.
متن کاملMetric Tensor Estimates, Geometric Convergence, and Inverse Boundary Problems
Three themes are treated in the results announced here. The first is the regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz bound on the mean curvature of the boundary. The second is the geometric convergence of a (sub)sequence of manifolds with boundary with such geometrical bounds and a...
متن کامل