# Remarks on an overdetermined boundary value problem

## Related Articles

- Stress concentration in a spherical shell with two neighboring circular holes. Chekhov, V.; Zakora, S. // Journal of Mathematical Sciences;Jan2012, Vol. 180 Issue 2, p91
We have solved analytically the problem of the stressed state in an isotropic shallow spherical shell with two circular holes. The cases of the close location of holes of both equal and unequal radii in the shell under the action of internal pressure have been investigated numerically. We have...

- Existence and symmetry of minimizers for nonconvex radially symmetric variational problems. Kr�mer, Stefan // Calculus of Variations & Partial Differential Equations;Jun2008, Vol. 32 Issue 2, p219
We study functionals of the form where u is a real valued function over the ball $$B_R(0)\subset {\mathbb{R}}^N$$ which vanishes on the boundary and W is nonconvex. The functional is assumed to be radially symmetric in the sense that W only depends on $$|{\nabla u}|$$ . Existence of one and...

- Fractional extensions of some boundary value problems in oil strata. Mridula, Garg; Rao, Alka // Proceedings of the Indian Academy of Sciences: Mathematical Scie;May2007, Vol. 117 Issue 2, p267
In the present paper, we solve three boundary value problems related to the temperature field in oil strata -- the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the...

- Asymptotics of the solution of Laplace's equation with mixed boundary conditions. Ershov, A. A. // Computational Mathematics & Mathematical Physics;Jun2011, Vol. 51 Issue 6, p994
uniform asymptotic expansion of the solution of a two-dimensional elliptic problem with mixed boundary conditions is found. A physical application of the result is discussed.

- The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance. Xiaoling Han; Ting Wang // International Journal of Differential Equations;2011, p1
We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.

- On one boundary-value problem for the Laplace equation. Martynenko, I. // Journal of Engineering Physics & Thermophysics;Mar2007, Vol. 80 Issue 2, p420
We have derived a Fredholm-type equation of the second kind for a directional derivative problem arising in the stationary theory of heat conduction. One result of Ya. B. Lopatinskii has been refined.

- Increasing smoothness of solutions to a hyperbolic system on the plane with delay in the boundary conditions. Lyul'ko, N. A. // Siberian Mathematical Journal;Nov2008, Vol. 49 Issue 6, p1062
Under consideration is a mixed problem in the half-strip Î = {( x, t): 0 < x < 1, t > 0} for a first order homogeneous linear hyperbolic system with delay in t in the boundary conditions. We study the behavior of the Laplace transform of a solution to this problem for the large values of the...

- An analytic mapping of 3-D space to facilitate physical analysis. Bloor, M. I. G.; Wilson, M. J. // Computing;Mar2007, Vol. 79 Issue 2-4, p381
A method is presented for the solution of Laplace's equation in three dimensions through the use of a combination of polynomial and eigenfunction solutions. Results are presented comparing the method with an exact solution. Excellent agreement is obtained for economical solution representations....

- On the singularities of the gradient of the solution to the Dirichlet-Neumann problem outside a plane cut. Krutitskii, P.; Sgibnev, A. // Mathematical Notes;Mar/Apr2005, Vol. 77 Issue 3/4, p335
The problem considered in this paper deals with the Laplace equation outside a cut of sufficiently arbitrary form. The Dirichlet condition is given on one side of the cut and the Neumann condition on the other. Using the integral representation for the solution, we obtain explicit asymptotic...