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Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2016, Volume 368, Issue 9, pp. 6227 - 6252
We consider second order uniformly elliptic operators of divergence form in \mathbb{R}^{d+1} H^s(\mathbb{R}^d) . Moreover, we also show a factorization formula... 
Dirichlet-Neumann maps | CALCULUS | EQUATIONS | PSEUDODIFFERENTIAL-OPERATORS | DIRAC OPERATORS | ABSOLUTE CONTINUITY | L-P | LAYER POTENTIALS | Divergence form elliptic operators | MATHEMATICS | BILINEAR ESTIMATE | NONSMOOTH COEFFICIENTS | Poisson operators | DOMAINS
Journal Article
SIAM JOURNAL ON NUMERICAL ANALYSIS, ISSN 0036-1429, 2019, Volume 57, Issue 3, pp. 1183 - 1204
The computation of the Dirichlet-Neumann operator for the Laplace equation is the primary challenge for the numerical simulation of the ideal fluid equations.... 
Zernike polynomials | WATER-WAVES | MATHEMATICS, APPLIED | POLAR | EQUATIONS | SURFACE | Euler equations | Dirichlet-Neumann operator
Journal Article
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 04/2018, Volume 474, Issue 2212, p. 20170704
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2009, Volume 247, Issue 5, pp. 1354 - 1396
Journal Article
Inverse Problems, ISSN 0266-5611, 07/2017, Volume 33, Issue 9, p. 95001
In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schrodinger operator in dimension... 
Carleman estimates | DirichletNeumann map | complex geometric optics solutions | RiemannLebesgue lemma | fourier transform | Magnetic Schrödinger operator | MATHEMATICS, APPLIED | Riemann-Lebesgue lemma | INVERSE PROBLEM | Dirichlet-Neumann map | Magnetic Schrodinger operator | PHYSICS, MATHEMATICAL | EQUATION | UNIQUENESS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 8/2008, Volume 360, Issue 8, pp. 3945 - 3973
Operators of the form A = a(x,D) + K with a pseudodifferential symbol a(x,ξ) belonging to the Hörmander class $S_{1,\delta}^{m}$ , m > 0, 0 ≤ δ < 1, and... 
Mathematical manifolds | Riemann manifold | Differential operators | Evolution equations | Fourier transformations | Coordinate systems | Calculus | Banach space | Sobolev spaces | Dirichlet-Neumann operator | Bounded H∞-calculus | Pseudodifferential operators
Journal Article
INVERSE PROBLEMS AND IMAGING, ISSN 1930-8337, 12/2018, Volume 12, Issue 6, pp. 1309 - 1342
In this paper we study local stability estimates for a magnetic Schrodinger operator with partial data on an open bounded set in dimension n >= 3. This is the... 
MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | INVERSE PROBLEM | magnetic Schrodinger operator | Dirichlet-Neumann map | Carleman estimates | CALDERON PROBLEM | PHYSICS, MATHEMATICAL | complex geometric optic solutions | Inverse problems | Radon transform | PARTIAL CAUCHY DATA | EQUATION
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2016, Volume 321, pp. 414 - 434
We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the... 
Series expansion | Pseudo-spectral method | Dirichlet–Neumann operator | Solitary waves | Ferrofluid jet | Dirichlet-Neumann operator | DIRICHLET-NEUMANN OPERATORS | GRAVITY-WAVES | PHYSICS, MATHEMATICAL | FLOW | ANALYTICITY | WATER-WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DEEP-WATER | DOMAINS | SCATTERING | Magnetic fields | Analysis | Methods
Journal Article
Asymptotic Analysis, ISSN 0921-7134, 2017, Volume 104, Issue 3-4, pp. 103 - 106
We consider the elliptic estimates for the Dirichlet-Neumann operator related to the water waves problem on a two-dimensional corner domain in this paper. Due... 
corner domains | Elliptic estimate | water waves problem | Dirichlet-Neumann operator | PLANE DOMAINS | MATHEMATICS, APPLIED | 2ND-ORDER | GENERAL EDGE ASYMPTOTICS | BOUNDARY-VALUE-PROBLEMS | EQUATIONS | WELL-POSEDNESS | WAVES | STABLE ASYMPTOTICS | COEFFICIENTS | POINTS | Water waves | Dirichlet problem | Estimates
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2005, Volume 37, Issue 1, pp. 302 - 320
Journal Article
by Ming, M
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 10/2019, Volume 39, Issue 10, pp. 6039 - 6067
Based on the H-2 existence of the solution, we investigate weighted estimates for a mixed boundary elliptic system in a two-dimensional corner domain, when the... 
MATHEMATICS | MATHEMATICS, APPLIED | 2ND-ORDER | GENERAL EDGE ASYMPTOTICS | corner domain | mixed boundary problem | COEFFICIENTS | Weighted elliptic estimates | Dirichlet-Neumann operator
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 06/2001, Volume 170, Issue 1, pp. 276 - 298
In this paper we present results on the stability of perturbation methods for the evaluation of Dirichlet-Neumann operators (DNO) defined on domains that are... 
Dirichlet-Neumann operators | Numerical stability | Geometric perturbation methods | WATER-WAVES | IMPROVED FORMALISM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | geometric perturbation methods | GRAVITY-WAVES | BOUNDARY | ROUGH-SURFACE SCATTERING | PHYSICS, MATHEMATICAL | numerical stability | EQUATION
Journal Article
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 2008, Volume 360, Issue 8, pp. 3945 - 3973
Operators of the form A = a( x, D) + K with a pseudodifferential symbol a( x, xi) belonging to the Hormander class S-1,delta(m), m > 0, 0 <= delta < 1, and... 
MATHEMATICS | pseudodifferential operators | bounded H-infinity-calculus | Dirichlet-Neumann operator
Journal Article
ANALYSIS AND APPLICATIONS, ISSN 0219-5305, 04/2012, Volume 10, Issue 2
In this paper, we prove L-infinity-estimates for solutions of divergence operators in the case of mixed boundary conditions. In this very general setting, the... 
MATHEMATICS | MATHEMATICS, APPLIED | CAMPANATO SPACES | Elliptic equations | BOUNDARY-VALUE-PROBLEMS | L-infinity-estimates | NONSMOOTH DATA | mixed Dirichlet-Neumann conditions
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 3, pp. 906 - 920
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 3/2013, Volume 54, Issue 2, pp. 271 - 300
Under consideration is the Dirichlet-Neumann operator on the boundary of the distorted half-space bounded below by a surface which is close to a hyperplane. We... 
Mathematics, general | Mathematics | Dirichlet-Neumann operator | differential | MATHEMATICS | EQUATIONS | WATER-WAVES | WELL-POSEDNESS
Journal Article
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