Andriadze, T. I.; Criado, F. About mathematical model or some diffuse processes in the Mediterranean and exterior Poincare problem for the Helmholtz equation. (English) Zbl 0758.35026 Rev. R. Acad. Cienc. Exactas Fís. Nat. Madr. 84, No. 4, 589-599 (1990). Let \(S\subset E^ 2\) be a closed Lyapunov’s curve of \({\mathcal C}^{1,h}\) class and denote by \(D^ -\) the external region \((\infty\in D^ -)\). The authors investigate the following problem: finding the solution \(u\) of the Helmholtz equation \(\Delta u+c_ 0u=0\), \(c_ 0\) const., in \(D^ -\), possessing Hölder-continuous first derivatives in \(D^ -\cup S\) and satisfying the boundary condition \(l\cdot\lim_{z\to t_ 0,z\in D^ -}u(z)=f(t_ 0)\), \(t_ 0\in S\), where \(l(t_ 0)=(l_ 1(t_ 0),l_ 2(t_ 0))\) is a unit vector, \(f\) is a Hölder-continuous function on \(S\). Metaharmonic potentials are used for the solution of this problem. Reviewer: M.Brzezina (Ostrava) MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J25 Boundary value problems for second-order elliptic equations 31B35 Connections of harmonic functions with differential equations in higher dimensions Keywords:metaharmonic potential PDFBibTeX XMLCite \textit{T. I. Andriadze} and \textit{F. Criado}, Rev. R. Acad. Cienc. Exactas Fís. Nat. Madr. 84, No. 4, 589--599 (1990; Zbl 0758.35026) Full Text: EuDML