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Solution of the Robin problem for the Laplace equation

Dagmar Medková (1998)

Applications of Mathematics

For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series.

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Daftardar-Gejji, Varsha, Bhalekar, Sachin (2008)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 31B10In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method.* This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.

Symmetric and Zygmund measures in several variables

Evgueni Doubtsov, Artur Nicolau (2002)

Annales de l’institut Fourier

Let ω : ( 0 , ∞ ) → ( 0 , ∞ ) be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure μ ∈ ℝ n is called ω -Zygmund if there exists a positive constant C such that | μ ( Q + ) - μ ( Q - ) | ≤ C ω ( ℓ ( Q + ) ) | Q + | for any pair Q + , Q - ⊂ ℝ n of adjacent cubes of the same size. Similarly, μ is called an ω - symmetric measure if there exists a positive constant C such that | μ ( Q + ) / μ ( Q - ) - 1 | ≤ C ω ( ℓ ( Q + ) ) for any pair Q + , Q - ⊂ ℝ n of adjacent cubes of the same size, ℓ ( Q + ) = ℓ ( Q - ) < 1 . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...

The boundary-value problems for Laplace equation and domains with nonsmooth boundary

Dagmar Medková (1998)

Archivum Mathematicum

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.

The multiple layer potential for the biharmonic equation in n variables

Alberto Cialdea (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The definition of multiple layer potential for the biharmonic equation in R n is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.

The Neumann problem for the Laplace equation on general domains

Dagmar Medková (2007)

Czechoslovak Mathematical Journal

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 G 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 ∂ G . If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability...

The transmission problem with boundary conditions given by real measures

Dagmar Medková (2007)

Annales Polonici Mathematici

The unique solvability of the problem Δu = 0 in G⁺ ∪ G¯, u₊ - au_ = f on ∂G⁺, n⁺·∇u₊ - bn⁺·∇u_ = g on ∂G⁺ is proved. Here a, b are positive constants and g is a real measure. The solution is constructed using the boundary integral equation method.

Thinness and non-tangential limit associated to coupled PDE

Allami Benyaiche, Salma Ghiate (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ▵ 2 ϕ = 0 ) and equations of ▵ 2 ϕ = ϕ type.

Currently displaying 81 – 100 of 109