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36 results on '"Heck, Horst"'

1. Increasing stability for the inverse problem for the Schr\'odinger equation

Author

Choudhury, Anupam Pal and Heck, Horst

Subjects
Mathematics - Analysis of PDEs
Abstract

In this article, we study the increasing stability property for the determination of the potential in the Schr\"odinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat and homogeneous boundary condition is prescribed on this part. In contrast to earlier works, we are able to deal with the case when potentials have some Sobolev regularity and also need not be compactly supported inside the domain.

Published
2017
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2. Linear sampling method for identifying cavities in a heat conductor

Author

Heck, Horst, Nakamura, Gen, and Wang, Haibing

Subjects
Mathematical Physics
Abstract

We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a freedom to choose the time variable, which suggests that we have more data than the linear sampling methods for the inverse boundary value problem associated with EIT and inverse scattering problem with near field data.

Published
2011
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3. Optimal stability estimate of the inverse boundary value problem by partial measurements

Author

Heck, Horst and Wang, Jenn-Nan

Subjects
Mathematics - Analysis of PDEs
Abstract

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent, improves our former result on the partial data problem in which log-log-type estimates were derived.

Published
2007

4. A Remark on Maximal Regularity of the Stokes Equations

Author

Geissert, Matthias, Heck, Horst, Escher, Joachim, editor, Guidotti, Patrick, editor, Hieber, Matthias, editor, Mucha, Piotr, editor, Prüss, Jan W., editor, Shibata, Yoshihiro, editor, Simonett, Gieri, editor, Walker, Christoph, editor, and Zajaczkowski, Wojciech, editor

Published
2011
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5. On the Equation div u = g and Bogovskii’s Operator in Sobolev Spaces of Negative Order

Author

Geißert, Matthias, Heck, Horst, Hieber, Matthias, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Curto, R. E., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevsky, V., editor, Putinar, M., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Lunel, S. M. Verduyn, editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, Koelink, Erik, editor, van Neerven, Jan, editor, de Pagter, Ben, editor, Sweers, Guido, editor, Luger, Annemarie, editor, and Woracek, Harald, editor

Published
2006
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10. Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates

Author

Choudhury, Anupam Pal, Heck, Horst, Choudhury, Anupam Pal, and Heck, Horst

Abstract

In this article, we establish logarithmic stability estimates for the determination of the perturbation of the biharmonic operator from partial data measurements when the inaccessible part of the domain is flat and homogeneous boundary conditions are assumed on this part. This is an improvement to a log-log type stability estimate proved earlier for the partial data case.

Published
2021

17. Increasing stability for the inverse problem for the Schrödinger equation.

Author

Pal Choudhury, Anupam and Heck, Horst

Subjects
*SCHRODINGER equation, *MANIFOLDS (Mathematics), *FINITE fields, *GROUP theory, *GALERKIN methods
Abstract

In this article, we study the increasing stability property for the determination of the potential in the Schrödinger equation from partial data. We shall assume that the inaccessible part of the boundary is flat, and homogeneous boundary condition is prescribed on this part. In contrast to earlier works, we are able to deal with the case when potentials have some Sobolev regularity and also need not be compactly supported inside the domain. [ABSTRACT FROM AUTHOR]

Published
2018
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18. Reconstruction of obstacles immersed in an incompressible fluid

Author

Heck, Horst, Uhlmann, Gunther, Wang, Jenn-Nan, Heck, Horst, Uhlmann, Gunther, and Wang, Jenn-Nan

Abstract

We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokes equation with a variable viscosity.

Published
2007

19. The Ornstein-Uhlenbeck semigroup in exterior domains

Author

Geissert, Matthias, Heck, Horst, Hieber, Matthias, Wood, Ian, Geissert, Matthias, Heck, Horst, Hieber, Matthias, and Wood, Ian

Abstract

Let Omega be an exterior domain in R^n. It is shown that Ornstein-Uhlenbeck operators L generate C_0-semigroups on L^p(Omega) for p in (1, \infty) provided Omega is smooth. The method presented also allows to determine the domain D(L) of L and to prove L^p-L^q smoothing properties of e^{tL}. If Omega is only Lipschitz, results of this type are shown to be true for p close to 2.

Published
2005

29. H∞-CALCULUS FOR A SYSTEM OF LAPLACE OPERATORS WITH MIXED ORDER BOUNDARY CONDITIONS.

Author

GEISSERT, MATTHIAS, HECK, HORST, and TRUNK, CHRISTOF

Subjects
CALCULUS, MATHEMATICAL analysis, LAPLACE'S equation, PARTIAL differential equations, BOUNDARY value problems
Abstract

In this paper we prove that the Lp realisation of a system of Laplace operators subjected to mixed first and zero order boundary conditions admits a bounded H∞-calculus. Furthermore, we apply this result to the Magnetohydrodynamic equation with perfectly conducting wall condition. [ABSTRACT FROM AUTHOR]

Published
2013
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33. Lp-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Author

Geissert, Matthias, Heck, Horst, and Hieber, Matthias

Abstract

Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C0-semigroup on Lσp(Ω), 1 < p < ∞, with generator . Moreover, for and initial data u0 ∈ Lσp(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

Published
2006
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35. Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates

Author

Choudhury, Anupam Pal, Heck, Horst, Choudhury, Anupam Pal, and Heck, Horst

Abstract

In this article, we establish logarithmic stability estimates for the determination of the perturbation of the biharmonic operator from partial data measurements when the inaccessible part of the domain is flat and homogeneous boundary conditions are assumed on this part. This is an improvement to a log-log type stability estimate proved earlier for the partial data case.

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