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极小变分流牛曼问题的弱解的存在性 被引量：2

Existence of Weak Solutions for the Minimizing Total Variation Flow with Neumann Boundary Conditions
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摘要 利用Crandall-Liggett半群定理和完全增长算子的性质,得到初始值属于L2(Ω)的极小变分流第二边值问题弱解的存在性. Using Crandall-Liggett＇s semigroups generation theorem and the quality of the completely accretive operator, we conclude that the minimizing total variation flow with Neumann boundary conditions has weak solutions.
作者 芮杰 杨孝平
机构地区 中国石油大学数学与计算科学学院 南京理工大学理学院
出处 《应用泛函分析学报》 CSCD 2009年第4期356-362,共7页 Acta Analysis Functionalis Applicata
关键词 完全增长算子 半群解 极大单调算子 弱解 completely accretive operator mild solution maximal monotone operator weak solution
分类号 O175.29 [理学—基础数学]
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参考文献8

  • 1Andreu F, Ballester C, Caselles V, et al. Minimizing total variation flow[J]. Diff Int Eqs,2001,4(3): 321-360.
  • 2Andreu F, Ballester C, Caselles V, et al. The Dirichlet problem for the total variation flow[J].J Funet, Anal ,2001,180(2) : 347-403.
  • 3Lin F H, Yang X P. Geometric Measure Theory[M]. Beijing-New York: Science Press-International Press, 2002.
  • 4Anzellotti G. Pairings between measures and bounded functions and compensated compactness[J]. Ann di Matematica Puraed Appl. Ⅳ, 1993,135 : 293-318.
  • 5Brezis H. Operateurs Maximaux Monotones[M]. North Holland, Amsterdam: 1973.
  • 6Andreu F, Mazon J M, Segura S, et al. Quasilinear elliptic and parabolic equations in L^1 with nonlinear boundary conditions[J]. Adv in Math Sci and Appl, 1977,7 : 183-213.
  • 7Crandall M G, Liggett T M. Generation of semigroups of nonlinear transformations on general Banach spaees[J].Amer J Math,1971,93:265-298.
  • 8Ph Benilan, Crandall M G. Completely accretive operators, in semigroups theory and evolution equations [J]. Lecture Notes Pure Appl Math, Marcel Dekker, 1991 : 41-76.

同被引文献24

  • 1Chambolle A, Lions P L. Image recovery via total variation minimization and related problems. Numer Math, 1997, 76:167-188.
  • 2Vese L. A study in the BV space of a denoising-deblurring variational problem. Applied Mathematics and Optimization, 2001, 44(2): 131-161.
  • 3Giaquinta M, Modica G, Soucek J. Functionals with linear growth in the calculus of variations. Comment Math Univ Carolinae, 1979, 20:143-156.
  • 4Andreu F, Ballester C, Caselles V, Mazon J M. The Dirichlet problem for the total variation flow. J Funct Anal, 2001, 180(2): 347-403.
  • 5Andreu F, Ballester C, Caselles V, Mazon J M. Minimizing total variation flow. Diff Int Eqs, 2001, 4(3): 321-360.
  • 6Lin F H, Yang X P. Geometric Measure Theory. Beijing, New York: Science Press-International Press, 2002.
  • 7Anzellotti G. Pairings between measures and bounded functions and compensated compactness. Ann di Matematica Pura ed Appl, 1993, 135(4): 293-318.
  • 8Crandall M G, Liggett T M. Generation of semigroups of nonlinear transformations on general Banach spaces. Amer J Math, 1971, 93:265-298.
  • 9Anzellotti G. The Euler equation for functionals with linear growth. Trans Amer Math Soc, 1985, 290: 483-501.
  • 10Lichenwski A,Teman R. Pseudosolutions of the time dependent minimal surface problem[J].Journal of Differential Equations,1978.340-364.

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应用泛函分析学报
2009年 第4期

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