Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

Mikhail Borsuk; Damian Wiśniewski

Open Mathematics (2012)

  • Volume: 10, Issue: 6, page 2051-2072
  • ISSN: 2391-5455

Abstract

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We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.

How to cite

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Mikhail Borsuk, and Damian Wiśniewski. "Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains." Open Mathematics 10.6 (2012): 2051-2072. <http://eudml.org/doc/269079>.

@article{MikhailBorsuk2012,
abstract = {We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.},
author = {Mikhail Borsuk, Damian Wiśniewski},
journal = {Open Mathematics},
keywords = {Elliptic divergence quasi-linear equations; Weak solutions; Unbounded domains; elliptic divergence quasi-linear equation; weak solution; unbounded domain},
language = {eng},
number = {6},
pages = {2051-2072},
title = {Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains},
url = {http://eudml.org/doc/269079},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Mikhail Borsuk
AU - Damian Wiśniewski
TI - Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 2051
EP - 2072
AB - We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
LA - eng
KW - Elliptic divergence quasi-linear equations; Weak solutions; Unbounded domains; elliptic divergence quasi-linear equation; weak solution; unbounded domain
UR - http://eudml.org/doc/269079
ER -

References

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  1. [1] Borsuk M.V., A priori estimates and solvability of second order quasilinear elliptic equations in a composite domain with nonlinear boundary condition and conjugacy condition, Trudy Mat. Inst. Steklov., 1968, 103, 15–50 (in Russian) Zbl0202.11502
  2. [2] Borsuk M., Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains, Front. Math., Birkhäuser/Springer, Basel, 2010 
  3. [3] Borsuk M., Kondratiev V., Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, North-Holland Math. Library, 69, Elsevier, Amsterdam, 2006 Zbl1246.35004
  4. [4] Furusho Ya., Existence of global positive solutions of quasilinear elliptic equations in unbounded domains, Funkcial. Ekvac., 1989, 32(2), 227–242 Zbl0694.35065
  5. [5] Gel’fand I.M., Shilov G.E., Generalized Functions I, Academic Press, New York, 1964 
  6. [6] Kondratiev V., Liskevich V., Moroz V., Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2005, 22(1), 25–43 http://dx.doi.org/10.1016/j.anihpc.2004.03.003[Crossref] Zbl1130.35053
  7. [7] Lieberman G.M., Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal., 1988, 12(11), 1203–1219 http://dx.doi.org/10.1016/0362-546X(88)90053-3[Crossref] 
  8. [8] Noussair E.S., Swanson C.A., Decaying entire solutions of quasilinear elliptic equations, Funkcial. Ekvac., 1988, 31(3), 415–438 Zbl0684.35036
  9. [9] Ouassarah A.A., Hajjaj A., Existence of solutions for quasilinear elliptic boundary value problems in unbounded domains, Bull. Belg. Math. Soc. Simon Stevin, 1996, 3(2), 215–223 Zbl0848.35045
  10. [10] Pao C.V., Nonlinear elliptic boundary value problems in unbounded domains, Nonlinear Anal., 1992, 18(8), 759–774 http://dx.doi.org/10.1016/0362-546X(92)90170-J[Crossref] 
  11. [11] Rivkind V.Ja., Uralćeva N.N., Classical solvability and linear schemes for the approximate solution of diffraction problems for quasilinear equations of parabolic and of elliptic type, In: Problems of Mathematical Analysis III, Integral and Differential Equations, Leningrad University, Leningrad, 1972, 69–111 (in Russian) 
  12. [12] Wisniewski D., Boundary value problems for a second-order elliptic equation in unbounded domains, Ann. Univ. Paedagog. Crac. Stud. Math., 2010, 9, 87–122 Zbl1222.35077

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