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

• Autorzy: Mikhail Borsuk , Damian Wiśniewski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Elliptic divergence quasi-linear equations; Weak solutions; Unbounded domains

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2051-2072

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Mikhail Borsuk

• Department of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, Słoneczna 54, 10-957, Olsztyn-Kortowo, Poland,

autor

Damian Wiśniewski

• Department of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, Słoneczna 54, 10-957, Olsztyn-Kortowo, Poland,

Bibliografia

• [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)
• [2] Borsuk M., Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains, Front. Math., Birkhäuser/Springer, Basel, 2010
• [3] Borsuk M., Kondratiev V., Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, North-Holland Math. Library, 69, Elsevier, Amsterdam, 2006
• [4] Furusho Ya., Existence of global positive solutions of quasilinear elliptic equations in unbounded domains, Funkcial. Ekvac., 1989, 32(2), 227–242
• [5] Gel’fand I.M., Shilov G.E., Generalized Functions I, Academic Press, New York, 1964
• [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]
• [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] Noussair E.S., Swanson C.A., Decaying entire solutions of quasilinear elliptic equations, Funkcial. Ekvac., 1988, 31(3), 415–438
• [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
• [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] 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] Wisniewski D., Boundary value problems for a second-order elliptic equation in unbounded domains, Ann. Univ. Paedagog. Crac. Stud. Math., 2010, 9, 87–122

Identyfikatory

DOI

10.2478/s11533-012-0127-2