Abstract
Normalization results are obtained for classes of second-order elliptic equations in \(\mathbb{R}\)which degenerate along a simple closed curve or with an isolated singularity. The behavior of the solutions of the corresponding homogeneous equation in a neighborhood of the degeneracy as well as the maximum principle is studied.
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Mathematics Subject Classification (2000). Primary 35J70; Secondary 35A05, 35B50.
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References
P. Cordaro and X. Gong: Normalization of complex-valued vector fields which degenerate along a real curve, Adv. Math., Vol. 184, 89–118, (2004).
A. Dzhuraev: Singular Partial Differential Equations, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Vol. 1-09, (2000).
A. Meziani: On planar elliptic structures with infinite type degeneracy, J. Funct. Anal., Vol. 179(2), 333–373, (2001).
A. Meziani: Representation of solutions of a singular Cauchy-Riemann equation in the plane, Complex Var. Elliptic Equ., Vol. 53(12), 1111–1130, (2008).
A. Meziani: Properties of solutions of a planar second order elliptic equation with a singularity, Complex Var. Elliptic Equ., Vol. 54(7), 677–688, (2009).
A. Meziani: On first and second order planar elliptic equations with degeneracies, arXiv. org, arXiv:0910.0539v1 (74 pages), (2009).
Z.D. Usmanov: On characteristics of solutions to an elliptic model equation with a singularity on a part of the boundary, Complex Var. Elliptic Equ., Vol. 53(4), 377–381, (2008).
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Meziani, A. (2012). Behavior of a Class of Second-order Planar Elliptic Equations with Degeneracies. In: Ball, J., Curto, R., Grudsky, S., Helton, J., Quiroga-Barranco, R., Vasilevski, N. (eds) Recent Progress in Operator Theory and Its Applications. Operator Theory: Advances and Applications(), vol 220. Springer, Basel. https://doi.org/10.1007/978-3-0348-0346-5_14
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DOI: https://doi.org/10.1007/978-3-0348-0346-5_14
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