2 edition of **Polar sets and removable singularities of partial differential equations.** found in the catalog.

Polar sets and removable singularities of partial differential equations.

Walter Littman

- 384 Want to read
- 29 Currently reading

Published
**1967**
by Almqvist & Wiksell in Stockholm
.

Written in English

- Differential equations, Partial.

**Edition Notes**

Bibliography: p. 9.

Series | Arkiv för Matematik,, bd. 7, nr. 1 |

Classifications | |
---|---|

LC Classifications | QA3 .A7 bd. 7, nr. 1 |

The Physical Object | |

Pagination | 9 p. |

ID Numbers | |

Open Library | OL5160615M |

LC Control Number | 74497859 |

Abstract: Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on. Pure Math., Vol. IV, American Mathematical Society, Providence, R.I., , pp. 33– MR ; Bent Fuglede (), Reese Harvey and John Polking, Removable singularities of solutions of linear partial differential equations, Acta Math Polar sets and removable singularities of partial differential equations.

Singularities of Solutions of Second-Order Quasilinear Equations by Laurent Veron, , available at Book Depository with free delivery worldwide. Ordinary Differential Equations (Dover Books on Mathematics) Morris Tenenbaum. out of 5 stars Paperback. Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics) A History of Algebraic and Differential Topology, - .

Books. Publishing Support. Login. W. Littman Polar sets and removable singularities of partial differential equations Ark. Mat. 7 Crossref MathSciNet Google Scholar R. Harvey and J. Polking Removable singularities of solutions of linear partial differential equations Acta Math. Crossref MathSciNet Google Scholar. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area : Peter D. Lax.

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Polar sets and removable singularities of partial differential equations By WALTER LITTMAN O. Introduction The question of removable singularities for partial differential equations is essen- tially the following: If u is a solution of such an equation in a domain V c R = with.

Logarithmic singularities of solutions to nonlinear partial differential equations TAHARA, Hidetoshi and YAMANE, Hideshi, Journal of the Mathematical Society of Japan, Potential estimates for a class of fully nonlinear elliptic equations Labutin, Denis A., Duke Mathematical Journal, Cited by: Polar sets and removable singularities of partial differential equations Walter Littman 1 Arkiv för Matematik volume 7, Article number: 1 () Cite this articleCited by: adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.

On Complex Singularity Analysis for Some Linear Partial Differential Equations in ℂ 3 Lastra, A., Malek, S., and Stenger, C., Abstract and Applied Analysis, Removable singularities of holomorphic solutions of linear partial differential equations IGARI, Katsuju, Journal of the Mathematical Society of Japan, Cited by: For some kernels in potential theory these conditions permit to characterize geometrically those sets which contain support of a nontrivial measure whose potential belongs to a given class of functions.

Several applications concerning removability of singularities of partial differential equations. Alborova and S. Vodop'yanov, “On removable singularities of bounded solutions for a class of quasielliptic equations,” in: Abstracts of Reports to the Eleventh All-Union School on Operator Theory in Function Spaces (Chelyabinsk, May, ) [in Russian], Part 3, Chelyabinsk (), p.

Suppose [equation] is a linear partial differential operator defined on an open set ⋂ ⊂ ℝ n, and that A ⊂ ⋂ is closed. A Survey of Removable Singularities | SpringerLink Skip to main content. Elliptic Equation Bounded Solution Quasilinear Elliptic Equation Removable Singularity These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm improves. REMOVABLE SINGULARITIES OF SOLUTIONS OF NONLINEAR SINGULAR PARTIAL DIFFERENTIAL EQUATIONS HIDETOSHI TAHARA Department of Mathematics, Sophia University Kioicho, Chiyoda-ku, Tokyo, Japan E-mail: [email protected] 1.

Introduction. The study of singularities has been one of the main subjects of research in partial di erential. The purpose of this paper is to use the geometrical theory of nonlinear partial differential equations and the theory of singularities of maps in order to obtain the general scheme for.

This paper is an overview of results devoted to metric conditions for removability of closed sets for solutions of homogeneous partial differential equations in various function classes. Acad. Sci. Paris, t. Skrie I, p.iquations aux d&i&es partielles/Partia/ Differential Equations On removable lateral singularities for quasilinear parabolic PDE Sergei E.

KUZNETSOV (l) Central Ec-on.-Math. Institute, Russian Academy of Scirnces. 32 Krasikowa, MoscowRussia. Current address: Department of. See [36] for an exhaustive survey on removable sets for elliptic operators in the C 1,α class.

To our aim, as we need to remove a singularity about a constant mean curvature equation, it would be. Polar set and removability. For the purposes of dealing with removable singularities, it is convenient to limit our attention to a restricted class of “polar sets” for the equations that we consider.

Definition C ∞ − (μ, Λ, k, Ω) Polar Set. Let 0. Nonlinear Analysis, Theory, Methods & Applications, Vol. 18, No. 9, pp.X/92 $+ Printed in Great Britain. Pergamon Press Ltd REMOVABLE SINGULARITIES OF A CLASS OF FULLY NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS P. POPIVANOV Mathematical Institute of the Bulgarian Academy of Sciences, Sofia, Bulgaria (Received 1.

Reflection, removable singularities, and approximation for partial differential equations, Part 1* By LEON EHRENPREIS 1. Introduction The general problem we deal with goes as follows: Let (', *D, I2 be regions in RI and let D3 = (Di, **, Do) be linear differential operators with constant coefficients.

(It is allowed that some (2 = (2' or that some D'. Removable singularities of solutions of semi-elliptic equations Article in Differential Equations 45(2) February with 5 Reads How we measure 'reads'.

ample of an application of analytic methods is the description of polar sets, which can be derived from the characterization of removable singularities for the corresponding partial di erential equation. In the reverse direction, Wiener’s test for the Brownian snake yields a characterization of those domains in which there exists a positive.

A Hausdorff measure classification of polar lateral boundary sets for superdiffusions Article in Mathematical Proceedings of the Cambridge Philosophical Society (03) - May with.

[29] W. Littman, Polar sets and removable singularities of partial differential equations, Ark. Mat. 7 () 1–9. Crossref, ISI, Google Scholar [30] V. G. Maz’ya, Sobolev Spaces with Applications to Elliptic Partial Differential Equations, 2nd edn.

(Springer, ). Crossref, Google Scholar.Suppose 1differential operator in R d andDis a bounded smooth domain in R Q = R + ×Dand letΓbe a compact set on the lateral boundary of prove thatΓis a removable lateral singularity for the equationu+Lu=u α in Q if and only if Cap 1/α, 2/α, α′ (Γ)=0 where Cap stands for the Besov capacity on the boundary.Bearing in mind the results on isolated singularities of elliptic partial differential equations of second order, one may conjecture that for a fourth-order partial differential equation as () the singularity may be removed if the solution is C 3 at the origin.