Green’s theorem from the viewpoint of applications. (English) Zbl 1060.35504

Ženíšek, Alexander

Appl. Math., Praha 44, No. 1, 55-80 (1999).

The paper contains a new detailed proof of Green’s theorem for functions from the Sobolev space \(W^{1,p}\), \(1\leq p < \infty \), defined on bounded two-dimensional domains with a Lipschitz continuous boundary. A special attention is paid to internal an external cusp-points. Line integrals are defined in a natural way without any use of partition of the unity. Divergence forms of Green’s theorem are proved in detail as well.

Reviewer: Michal Křížek (Praha)

MSC:

35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
26B20	Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
35J20	Variational methods for second-order elliptic equations
65N99	Numerical methods for partial differential equations, boundary value problems

Keywords:

Green’s theorem; elliptic problems; variational problems

References:

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[5]	J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques. Academia, Prague, 1967. · Zbl 1225.35003