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Keywords:
Neumann problem; degenerate elliptic equations
Neumann problem; degenerate elliptic equations
Summary:
In the paper we study the equation $Lu=f$, where $L$ is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set ${\Omega }$. We prove existence and uniqueness of solutions in the space $H(\Omega )$ for the Neumann problem.
References:
[1] S. Chanillo, R. L. Wheeden: Harnack’s inequalities and mean-value inequalities for solutions of degenerate elliptic equations. Commun. PDE 11 (1986), 1111–1134. DOI 10.1080/03605308608820458 | MR 0847996
[2] S. Chanillo, R. L. Wheeden: Existence and estimates for Green’s function for degenerate elliptic equations. Ann. Sc. Norm. Super. Pisa IV ser. 15, Fasc. II (1988), 309–340. MR 1007400
[3] B. Franchi, R. Serapioni: Pointwise estimates for a class of strongly degenerate elliptic operators: A geometrical approch. Ann. Sc. Norm. Sup. Pisa C1 ser. 14 (1987), 527–568. MR 0963489
[4] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function. Trans. Am. Math. Soc. 165 (1972), 207–226. DOI 10.1090/S0002-9947-1972-0293384-6 | MR 0293384 | Zbl 0236.26016
[5] A. Torchinsky: Real-Variable Methods in Harmonic Analysis. Academic Press, Orlando, 1986. MR 0869816 | Zbl 0621.42001
[6] A. Kufner, O. John, and S. Fučík: Function Spaces. Noordhoff International Publishing, Leyden, 1977. MR 0482102
[7] A. Kufner: Weighted Sobolev Spaces. John Wiley & Sons, New York, 1985. MR 0802206 | Zbl 0579.35021
[8] J. Heinonen, T. Kilpeläinen, and O. Martio: Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Math. Monographs. Clarendon Press, Oxford, 1993. MR 1207810
[9] J. Garcia-Cuerva, J. L. Rubio de Francia: Weighted Norm Inequalities and Related Topics. North-Holland Mathematics Studies 116. North Holland, Amsterdam-New York-Oxford, 1985. MR 0807149
[10] B. O. Turesson: Nonlinear Potential Theory and Weighted Sobolev Spaces. Lectures Notes in Mathematics Vol. 1736. Springer-Verlag, Berlin, 2000. MR 1774162
[11] V. Chiadò Piat, F. Serra Cassano: Relaxation of degenerate variational integrals. Nonlinear Anal., Theory Methods Appl. 22 (1994), 409–424. DOI 10.1016/0362-546X(94)90165-1 | MR 1266369
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