MR2126328
Kračmar, S. and Penel, P.
S. KRAČMAR and P. PENEL
Variational Properties of a Generic Model Equation in Exterior 3D Domains
Funkcialaj Ekvacioj. Serio Internacia
47
2004
499--523
http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-3/47_499.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2126328
We study a generic model equation in an exterior domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type.
Existence, Uniqueness, Variational Method, Anisotropically weighted Sobolev spaces.
Primary 35J20; Secondary 35D05, 35B45.
47-499
2004
Variational Properties of a Generic Model Equation in Exterior 3D Domains
KRAČMAR, S. and PENEL, P.
S. KRAČMAR and P. PENEL
1
Adams, R. A.
Sobolev Spaces
Academic Press, New York
1975
MR0450957
2
Farwig, R.
A variational approach in weighted Sobolev spaces to the operator $-\Delta+\partial/\partial_1$ in exterior domains of $R^3$
Mathematische Zeitschrift
210
1992
449-464
MR1171183
3
Farwig, R.
The stationary exterior 3-D problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces
Mathematische Zeitschrift
211
1992
409-447
MR1190220
4
Finn, R.
Estimates at infinity for stationary solutions of the Navier-Stokes equations
Bult. Math. de la Soc. Sci. Math. de la R.P.R. Tome 3
53
1959
387-418
MR0166495
5
Finn, R.
On the Exterior Stationary Problem for the Navier-Stokes Equations, and Associated Perturbation Problems
Arch. Rat. Mech. Anal.
19
1965
363-406
MR0182816
6
Hishida, T.
The Stokes operator with rotation effect in exterior domains
Analysis
19
1999
51-67
MR1690643
7
Impagliazzo, J.-L., Resolution des equations de Navier-Stokes compressibles a l'aide de la methode de decomposition, These de doctorat de l'Universite de Toulon et du Var, 1997
8
Kobayashi, T.; Shibata, Y.
On the Oseen equation in the three-dimensional exterior domains
Math. Ann.
310
1998
1-45
MR1600022
9
Kufner, A.
Weighted Sobolev Spaces
BSB B. G. Teubner Verlagsgesellschaft, Leipzig
1980
MR0664599
10
Kračmar, S.; Novotný, A.; Pokorný, M.
Estimates of three dimensional Oseen kernels in weighted $L^p$ spaces
In: "Applied Nonlinear Analysis", London-New York, Plenum Publishers/Kluwer Academic
1999
281-316
MR1727455
11
Kračmar, S.; Novotný, A.; Pokorný, M.
Estimates of Oseen kernels in weighted $L^p$ spaces
J. Math. Soc. Japan
53
2001
59-111
MR1800524
12
Nečasová, Š., Asymptotic properties of the steady fall of a body in a viscous fluid, Mathem. Models and Appl. (to appear)
MR2099812
13
Novotný, A.; Pokorný, M.
Three-dimensional steady flow of viscoelastic fluid past an obstacle
J. Math. Fluid Mech.
2
2000
294-314
MR1781917
14
Novotný, A.; Pokorný, M.
Steady plane flow of viscoelastic fluid past an obstacle
Applications of Math.
47
2002
231-254
MR1900513
15
Oseen, C. W.
Neuere Methoden und Ergebnisse in der Hydrodynamik
Leipzig, Akad. Verlagsgesellschaft M.B.H.
1927
MR1549558
16
Rudin, W.
Real and Complex Analysis, second edition
McGraw-Hill, New York
1974
MR0344043
17
Smith, D.
Estimates at Infinity for Stationary Solutions of the Navier-Stokes Equations in Two Dimensions
Arch. Rat. Mech. Anal.
20
1965
341-372
MR0185926
18
Turesson, B. O.
Nonlinear Potential Theory and Weighted Sobolev Spaces
Springer Verlag, New York
2000
MR1774162