Nonlinear Elliptic Equations for Measures

被引:5
作者
Tonoyan, L. G. [1 ]
机构
[1] Univ Alberta, Fac Sci, Dept Math & Stat Sci, Edmonton, AB, Canada
关键词
Vector Field; Probability Measure; Elliptic Equation; DOKLADY Mathematic; Nonlinear Elliptic Equation;
D O I
10.1134/S1064562411040132
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Nonlinear elliptic equations are studied for probability measures. It is supposed that a nonnegative Borel measure satisfies the weak elliptic equation, and it is found that for a fixed measure, this equation is linear. If measures are such that their densities locally uniformly converge to the density of a measure, then the functions converge on each ball. Since the measures are probability, it follows that the convergence of their densities implies convergence in variation. If the mappings are defined only for measures and satisfy certain conditions, then, in the class, the equation has a solution. The existence of a solution of the transport equation is ensured if the function k is continuous on the space of measures with the weak topology.
引用
收藏
页码:558 / 561
页数:4
相关论文
共 8 条
  • [1] Bogachev V, 2000, THEOR PROBAB APPL+, V45, P363, DOI 10.1137/S0040585X97978348
  • [2] Nonlinear evolution and transport equations for measures
    Bogachev, V. I.
    Roeckner, M.
    Shaposhnikov, S. V.
    [J]. DOKLADY MATHEMATICS, 2009, 80 (03) : 785 - 789
  • [3] Bogachev V. I., 2001, TEOR VEROYA PRIMEN, V46, P600
  • [4] On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions
    Bogachev, VI
    Krylov, NV
    Röckner, M
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (11-12) : 2037 - 2080
  • [5] Elliptic equations for measures on infinite dimensional spaces and applications
    Bogachev, VI
    Röckner, M
    [J]. PROBABILITY THEORY AND RELATED FIELDS, 2001, 120 (04) : 445 - 496
  • [6] Khasminskii R.Z., 1969, STABILITY SYSTEMS DI
  • [7] [Козлов Валерий Васильевич Kozlov Valerii Vasil'evich], 2008, [Успехи математических наук, Russian Mathematical Surveys, Uspekhi matematicheskikh nauk], V63, P93, DOI 10.4213/rm9216
  • [8] [Вершик Анатолий Моисеевич Vershik Anatolii Moiseevich], 2009, [Успехи математических наук, Russian Mathematical Surveys, Uspekhi matematicheskikh nauk], V64, P5, DOI 10.4213/rm9260