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Let $Ω$ be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problem $▵ u = - c u - d in Ω, u = 0 on \partial Ω .$ We prove two results: 1) If $Ω$ is not a ball and if one considers only solutions with $- c u - d \leq 0$ , then there exist at most finitely many pairs of coefficients $(c, d)$ so that the normal derivative $\frac{\partial u}{\partial ν} |_{\partial Ω}$ equals a given $ψ \neq 0$ .2) If one imposes no sign condition on the solutions but one additionally supposes that $Ω$ is sufficiently...

An inverse problem for time-harmonic electromagnetic currents in a smoothly layered medium.

Malmivuori, Markku (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

An inverse problem in a parabolic equation.

Li, Zhilin, Zheng, Kewang (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

An inverse problem of the wave equation.

J. Sjöstrand, A.G. Ramm (1991)

Mathematische Zeitschrift

An inversion of the obstacle problem and its explicit solution

Hans Lewy (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

An isoperimetric bound for a Sobolev constant

Philip S. Crooke (1978)

Colloquium Mathematicae

An Isoperimetric Inequality for the Principal Eigenvalue of a Periodic-Parabolic Problem.

Peter Hess (1987)

Mathematische Zeitschrift

An iteration method for controllability of semilinear parabolic equations.

Sun, Bo (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

An iteration method for nonlinear second order evolution equations

Konrad Gröger (1976)

Commentationes Mathematicae Universitatis Carolinae

An iterative method of alternating type for systems with special block matrices

Milan Práger (1991)

Applications of Mathematics

An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.

An $L^{1}$ -theory of existence and uniqueness of solutions of nonlinear elliptic equations

Philippe Bénilan, Lucio Boccardo, Thierry Gallouët, Ron Gariepy, Michel Pierre, Juan Luis Vazquez (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

An $L^{\infty}$ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials

Jim Jr. Douglas, Todd Dupont, Mary Fanett Wheeler (1974)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

An $L_{p}$ -analogue of the Vishik-Eskin theory.

Shargorodskij, Eugene (1994)

Memoirs on Differential Equations and Mathematical Physics

An $L^{p}$ -approach for the study of degenerate parabolic equations.

Labbas, Rabah, Medeghri, Ahmed, Sadallah, Boubaker-Khaled (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

An $L^{q} (L ²)$ -theory of the generalized Stokes resolvent system in infinite cylinders

Reinhard Farwig, Myong-Hwan Ri (2007)

Studia Mathematica

Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with $Σ \subset ℝ^{n - 1}$ , a bounded domain of class $C^{1, 1}$ , are obtained in the space $L^{q} (ℝ; L ² (Σ))$ , q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.

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