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Boundary value problem with inequalities for elliptic equations with degeneration
Pukalskyi Ivan 1
1 Department of Differential Equations, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords: boundary value problem, elliptic equations with degeneration
Abstract
Using the maximum principle and a priori estimates we study a boundary value problem  with inequalities for a second order elliptic equation with power singularities in the coefficients of an arbitrary order. We establish the existence and the uniqueness of the solution of the stated problem in Hölder spaces with a power weight.
References

[1] Duvaut G, Lions J.L. Les inéquations en mécanique et en physique. Dunod, Paris, 1972. – 384 p.

[2] Clowinski R., Lions J.L., Tremolieres R. Analyse numerique des inéquations variationnells, Dunod, Paris, 1976. – 574 p.

[3] Zeitz F. Modern theory of solid state. - M.L.: Gostekhizdat, 1949. - 736 p.

[4] Konakov P.K., Verevochkin T.E. Heat and mass transfer at obtaining single crystals. - M.:Metallurgy, 1971. - 387 p.

[5] Moiseev E.I. About solvability of one nonlocal boundary value problem // Diff. equations. -2001. - 37, № 11. - P. 1555-1567.

[6] Bitsadze A.B.Some classes of equations in partial derivatives. - M.: Nauka, 1981. - 448 p.

[7] Smirnov M.M. Growing elliptic and hyperbolic equations. - M.: Nauka, 1966. - 292 p.

[8] Matiychuk M.I. Parabolic and elliptic boundary value problems with features - Chernivtsi: Prut, 2003. - 248 p.

[9] Esteban Maria J. Nonexistence result for positive solutions of nonlinear elliptic degenerate problems // Nonlinear Anal. Theory Math. and Appl. – 1996, 26, № 4. – P. 835-843.

[10] Amano Kazuo. Maximum principle for degenerate elliptic-parabolic equations with Venttsel’s boundary conditions. – Trans. Amer. Math. Soc. – 1981. 263, № 2. – P. 377-396.

[11] Friedman A. Equations with partial derivatives of parabolic type. - M.: Mir, 1968. -427 p.

[12] Pukalsky I.D. Boundary value problems for nonuniformly parabolic and elliptic equations with degeneracy: Monograph. - Chernivtsi, 2008. - 253 p.

Cite
ACS Style
Pukalskyi, I. Boundary value problem with inequalities for elliptic equations with degeneration. Bukovinian Mathematical Journal. 2016, 1
AMA Style
Pukalskyi I. Boundary value problem with inequalities for elliptic equations with degeneration. Bukovinian Mathematical Journal. 2016; 1(3-4).
Chicago/Turabian Style
Ivan Pukalskyi. 2016. "Boundary value problem with inequalities for elliptic equations with degeneration". Bukovinian Mathematical Journal. 1 no. 3-4.
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