• 제목/요약/키워드: elliptic operators

검색결과 33건 처리시간 0.019초

CONSERVATIVE MINIMAL QUANTUM DYNAMICAL SEMIGROUPS GENERATED BY NONCOMMUTATIVE ELLIPTIC OPERATORS

  • Bahn, Chang-Soo;Ko, Chul-Ki
    • 대한수학회지
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    • 제42권6호
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    • pp.1231-1249
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    • 2005
  • By employing Chebotarev and Fagnola's sufficient conditions for conservativity of minimal quantum dynamical semigroups [7, 8], we construct the conservative minimal quantum dynamical semigroups generated by noncommutative elliptic operators in the sense of [2]. We apply our results to concrete examples.

UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY

  • Lee, Yong Hah
    • 대한수학회논문집
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    • 제32권4호
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    • pp.1025-1031
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    • 2017
  • We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

ZETA FUNCTIONS AND COEFFICIENTS OF AN ASYMPTOTIC EXPANSION OF logDet FOR ELLIPTIC OPERATORS WITH PARAMETER ON COMPACT MANIFOLDS

  • Lee, Yoonweon
    • Korean Journal of Mathematics
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    • 제7권2호
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    • pp.159-166
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    • 1999
  • For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.

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ELLIPTIC SYSTEMS INVOLVING COMPETING INTERACTIONS WITH NONLINEAR DIFFUSIONS II

  • Ahn, In-Kyung
    • 대한수학회논문집
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    • 제12권4호
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    • pp.869-880
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    • 1997
  • In this paper, we give sufficient conditions of certain elliptic systems involving competing iteractions with nonlinear diffusion rates. The existence of positive solution depends on the sign of the first eigenvalue of operators of Schr$\ddot{o}$dinger type. More precisely, if the sign of such operators are either both positive or both negative, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

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LONG TIME BEHAVIOR OF SOLUTIONS TO SEMILINEAR HYPERBOLIC EQUATIONS INVOLVING STRONGLY DEGENERATE ELLIPTIC DIFFERENTIAL OPERATORS

  • Luyen, Duong Trong;Yen, Phung Thi Kim
    • 대한수학회지
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    • 제58권5호
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    • pp.1279-1298
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    • 2021
  • The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

A CERTAIN EXAMPLE FOR A DE GIORGI CONJECTURE

  • Cho, Sungwon
    • 충청수학회지
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    • 제27권4호
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    • pp.763-769
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    • 2014
  • In this paper, we illustrate a counter example for the converse of a certain conjecture proposed by De Giorgi. De Giorgi suggested a series of conjectures, in which a certain integral condition for singularity or degeneracy of an elliptic operator is satisfied, the solutions are continuous. We construct some singular elliptic operators and solutions such that the integral condition does not hold, but the solutions are continuous.