A reaction-diffusion equation on a net-shaped thin domain
Thomas Elsken (2004)
Studia Mathematica
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Displaying similar documents to “Probabilistic Approach to the Neumann Problem for a Symmetric Operator”
A reaction-diffusion equation on a net-shaped thin domain
Multiplicity of positive solutions to second order differential equations with Neumann boundary conditions
Jifeng Chu, Daqing Jiang, Donal O'Regan, R. P. Agarwal (2005)
Applicationes Mathematicae
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We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.
Solution of the Neumann problem for the Laplace equation
Dagmar Medková (1998)
Czechoslovak Mathematical Journal
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For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.
The Neumann problem for the Laplace equation on general domains
Dagmar Medková (2007)
Czechoslovak Mathematical Journal
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The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on . If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on a necessary and sufficient condition for...
Continuous extendibility of solutions of the Neumann problem for the Laplace equation
Dagmar Medková (2003)
Czechoslovak Mathematical Journal
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A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given.
On continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition
Faragó, István, Korotov, Sergey, Szabó, Tamás
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In this work, we present and discuss continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition solved by the finite element and finite difference methods.
An Elliptic Neumann Problem with Subcritical Nonlinearity
Jan Chabrowski, Kyril Tintarev (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
On the Neumann problem with L¹ data
J. Chabrowski (2007)
Colloquium Mathematicae
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We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
On the Neumann problem with combined nonlinearities
Jan Chabrowski, Jianfu Yang (2005)
Annales Polonici Mathematici
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We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dagmar Medková (1998)
Archivum Mathematicum
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Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.