On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition

László Simon; Gisbert Stoyan

Applications of Mathematics (2001)

  • Volume: 46, Issue: 4, page 241-250
  • ISSN: 0862-7940

Abstract

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For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like u | Γ ∈ L 5 ( Γ ) ) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent q which is greater than 9 / 4 for the fourth power law.

How to cite

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Simon, László, and Stoyan, Gisbert. "On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition." Applications of Mathematics 46.4 (2001): 241-250. <http://eudml.org/doc/33086>.

@article{Simon2001,
abstract = {For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like $u\big |_\Gamma \in L_5(\Gamma )$) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent $q$ which is greater than $9/4$ for the fourth power law.},
author = {Simon, László, Stoyan, Gisbert},
journal = {Applications of Mathematics},
keywords = {radiation boundary condition; generalized solution; existence; nonlinear boundary condition; radiation boundary condition; elliptic equation; generalized solution; existence},
language = {eng},
number = {4},
pages = {241-250},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition},
url = {http://eudml.org/doc/33086},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Simon, László
AU - Stoyan, Gisbert
TI - On the existence of a generalized solution to a three-dimensional elliptic equation with radiation boundary condition
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 4
SP - 241
EP - 250
AB - For a second order elliptic equation with a nonlinear radiation-type boundary condition on the surface of a three-dimensional domain, we prove existence of generalized solutions without explicit conditions (like $u\big |_\Gamma \in L_5(\Gamma )$) on the trace of solutions. In the boundary condition, we admit polynomial growth of any fixed degree in the unknown solution, and the heat exchange and emissivity coefficients may vary along the radiating surface. Our generalized solution is contained in a Sobolev space with an exponent $q$ which is greater than $9/4$ for the fourth power law.
LA - eng
KW - radiation boundary condition; generalized solution; existence; nonlinear boundary condition; radiation boundary condition; elliptic equation; generalized solution; existence
UR - http://eudml.org/doc/33086
ER -

References

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