# Gradient method for non-injective operators in Hilbert space with application to Neumann problems

Applicationes Mathematicae (1999)

- Volume: 26, Issue: 3, page 333-346
- ISSN: 1233-7234

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topKarátson, János. "Gradient method for non-injective operators in Hilbert space with application to Neumann problems." Applicationes Mathematicae 26.3 (1999): 333-346. <http://eudml.org/doc/219243>.

@article{Karátson1999,

abstract = {The gradient method is developed for non-injective non-linear operators in Hilbert space that satisfy a translation invariance condition. The focus is on a class of non-differentiable operators. Linear convergence in norm is obtained. The method can be applied to quasilinear elliptic boundary value problems with Neumann boundary conditions.},

author = {Karátson, János},

journal = {Applicationes Mathematicae},

keywords = {Neumann boundary value problems; non-injective non-linear operator; gradient method; Hilbert space; noninjective nonlinear operators; translation invariance; nondifferentiable operators; linear convergence in norm; quasilinear elliptic boundary value problems; Neumann boundary conditions},

language = {eng},

number = {3},

pages = {333-346},

title = {Gradient method for non-injective operators in Hilbert space with application to Neumann problems},

url = {http://eudml.org/doc/219243},

volume = {26},

year = {1999},

}

TY - JOUR

AU - Karátson, János

TI - Gradient method for non-injective operators in Hilbert space with application to Neumann problems

JO - Applicationes Mathematicae

PY - 1999

VL - 26

IS - 3

SP - 333

EP - 346

AB - The gradient method is developed for non-injective non-linear operators in Hilbert space that satisfy a translation invariance condition. The focus is on a class of non-differentiable operators. Linear convergence in norm is obtained. The method can be applied to quasilinear elliptic boundary value problems with Neumann boundary conditions.

LA - eng

KW - Neumann boundary value problems; non-injective non-linear operator; gradient method; Hilbert space; noninjective nonlinear operators; translation invariance; nondifferentiable operators; linear convergence in norm; quasilinear elliptic boundary value problems; Neumann boundary conditions

UR - http://eudml.org/doc/219243

ER -

## References

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- [5] H. Gajewski, K. Gröger and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974. Zbl0289.47029
- [6] L. V. Kantorovich, On an effective method of solving extremal problems for quadratic functionals, Dokl. Akad. Nauk SSSR 48 (1945), 455-460.
- [7] L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, 1982. Zbl0484.46003
- [8] J. Karátson, The gradient method for non-differentiable operators in product Hilbert spaces and applications to elliptic systems of quasilinear differential equations, J. Appl. Anal. 3 (1997), 225-237. Zbl0899.46061
- [9] J. Nečas, Introduction to the Theory of Nonlinear Elliptic Equations, Wiley, 1986.
- [10] V. S. Vladimirov, A Collection of Problems on the Equations of Mathematical Physics, Mir, Moscow, 1986. Zbl0607.35001

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