Annali dell’Università di Ferrara

, Volume 47, Issue 1, pp 285–296 | Cite as

The modified jump problem for the Helmholtz equation

  • P. A. Krutitskii


The boundary value problem for the Helmholtz equation outside several cuts in a plane is studied. The 2 boundary conditions are given on the cuts. One of them specifies the jump of the unkown function. Another one contain the jump of the normal derivative of an unknown function and a limit value of this function on the cuts. The unique solution of this problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero by means of single layer and angular potentials. The singularities at the ends of the cuts are investigated.


Case Condition Neumann Problem Normal Derivative Fredholm Integral Equation Homogeneous Problem 


Nel presente lavoro si studia il problema al contorno per l'equazione di Helmholtz all'esterno di più tagli nel piano. Le due condizioni al contorno sono assegnate sui tagli. Una di queste prescrive il salto della funzione incognita, l'altra contiene il salto della derivata normale di una funzione incognita ed un valore limite di questa funzione sui tagli. La soluzione univoca di questo problema è ricondotta all'equazione di Fredholm di seconda specie ed indice zero, univocamente risolubiles, per mezzo dei potenziali di singolo strato ed angolare. Si studiano, inoltre, le singolarità agli estremi dei tagli.


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Copyright information

© Università degli Studi di Ferrara 2001

Authors and Affiliations

  • P. A. Krutitskii
    • 1
  1. 1.Dept. of Mathematics, Faculty of PhysicsMoscow State UniversityMoscowRussia

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