# Green's theorem from the viewpoint of applications

Applications of Mathematics (1999)

- Volume: 44, Issue: 1, page 55-80
- ISSN: 0862-7940

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topŽeníšek, Alexander. "Green's theorem from the viewpoint of applications." Applications of Mathematics 44.1 (1999): 55-80. <http://eudml.org/doc/33027>.

@article{Ženíšek1999,

abstract = {Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces $W^\{1,p\}()\equiv H^\{1,p\}()$$(1\le p<)$.},

author = {Ženíšek, Alexander},

journal = {Applications of Mathematics},

keywords = {Green’s theorem; elliptic problems; variational problems; Green's theorem; elliptic problems; variational problems},

language = {eng},

number = {1},

pages = {55-80},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Green's theorem from the viewpoint of applications},

url = {http://eudml.org/doc/33027},

volume = {44},

year = {1999},

}

TY - JOUR

AU - Ženíšek, Alexander

TI - Green's theorem from the viewpoint of applications

JO - Applications of Mathematics

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 44

IS - 1

SP - 55

EP - 80

AB - Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces $W^{1,p}()\equiv H^{1,p}()$$(1\le p<)$.

LA - eng

KW - Green’s theorem; elliptic problems; variational problems; Green's theorem; elliptic problems; variational problems

UR - http://eudml.org/doc/33027

ER -

## References

top- Differential and Integral Calculus I, Gostechizdat, Moscow, 1951. (Russian) (1951)
- Differential- und Integralrechnung I, VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. (1968) MR0238635
- An equilibrium finite element method in three-dimensional elasticity, Apl. Mat. 27 (1982), 46–75. (1982) MR0640139
- Function Spaces, Academia, Prague, 1977. (1977) MR0482102
- Les Méthodes Directes en Théorie des Equations Elliptiques, Academia, Prague, 1967. (1967) MR0227584

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