# Poisson-Boltzmann equation in ℝ³

Annales Polonici Mathematici (1991)

- Volume: 54, Issue: 2, page 125-134
- ISSN: 0066-2216

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topA. Krzywicki, and T. Nadzieja. "Poisson-Boltzmann equation in ℝ³." Annales Polonici Mathematici 54.2 (1991): 125-134. <http://eudml.org/doc/262418>.

@article{A1991,

abstract = {The electric potential u in a solute of electrolyte satisfies the equation
Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, $u|_\{∂Ω\} = 0$.
One studies the existence of a solution of the problem and its properties.},

author = {A. Krzywicki, T. Nadzieja},

journal = {Annales Polonici Mathematici},

keywords = {Poisson-Boltzmann equation; existence of solution; uniqueness; convergence; Dirichlet problems; existence},

language = {eng},

number = {2},

pages = {125-134},

title = {Poisson-Boltzmann equation in ℝ³},

url = {http://eudml.org/doc/262418},

volume = {54},

year = {1991},

}

TY - JOUR

AU - A. Krzywicki

AU - T. Nadzieja

TI - Poisson-Boltzmann equation in ℝ³

JO - Annales Polonici Mathematici

PY - 1991

VL - 54

IS - 2

SP - 125

EP - 134

AB - The electric potential u in a solute of electrolyte satisfies the equation
Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, $u|_{∂Ω} = 0$.
One studies the existence of a solution of the problem and its properties.

LA - eng

KW - Poisson-Boltzmann equation; existence of solution; uniqueness; convergence; Dirichlet problems; existence

UR - http://eudml.org/doc/262418

ER -

## References

top- [1] R. Courant, Partial Differential Equations, Interscience, New York London 1962. Zbl0099.29504
- [2] A. Friedman and K. Tintarev, Boundary asymptotics for solutions of the Poisson-Boltzmann equation, J. Differential Equations 69 (1987), 15-38. Zbl0637.35035
- [3] A. Krzywicki and T. Nadzieja, Radially symmetric Poisson-Boltzmann equation in a domain expanding to infinity, submitted. Zbl0722.34016
- [4] W. Pogorzelski, Integral Equations and their Applications, Pergamon Press and PWN, 1969.
- [5] I. Rubinstein, Counterion condensation as an exact limiting property of solution of the Poisson-Boltzmann equation, SIAM J. Appl. Math. 46 (1986), 1024-1038. Zbl0632.76106

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