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Direct and Inverse Problems in Potential Theory

In: Nonlinear Evolution Equations and Potential Theory

Author

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  • Gottfried Anger

    (MLU Halle, Sektion Mathematik, GDR)

Abstract

The aim of this paper is to sketch the most important direct problems (boundary value problems and initial value problems) of linear elliptic, parabolic and hyperbolic differential equations and some inverse problems corresponding to these equations. Both types of problems are divided into two classes. The first one is the class of properly posed problems, the other is the class of improperly posed problems. The Dirichlet problem for elliptic equations and parabolic equations and the Cauchy problem for hyperbolic equations are properly posed problems, the Dirichlet problem for hyperbolic equations and the inverse problem for the Laplace equation and the heat equation are improperly posed problems. There exist also inverse (improperly posed) problems concerning hyperbolic equations.

Suggested Citation

  • Gottfried Anger, 1975. "Direct and Inverse Problems in Potential Theory," Springer Books, in: Josef Král (ed.), Nonlinear Evolution Equations and Potential Theory, pages 11-44, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-4425-4_2
    DOI: 10.1007/978-1-4613-4425-4_2
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