Regularity of solutions to Kolmogorov equation with Gilbarg-Serrin matrix

被引:1
|
作者
Kinzebulatov, D. [1 ]
Semenov, Yu. A. [2 ]
机构
[1] Univ Laval, Dept Mathemat & Satist, 1045 Av Med, Quebec City, PQ G1V 0A6, Canada
[2] Univ Toronto, Dept Math, 40 St George Str, Toronto, ON M5S 2E4, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Elliptic operators; Form-bounded vector fields; Regularity of solutions; ELLIPTIC-OPERATORS; L-P; UNBOUNDED DIFFUSION; COEFFICIENTS; SPACES; GENERATION;
D O I
10.1007/s00028-022-00776-9
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In R-d, d >= 3, consider the divergence and the non-divergence form operators -Delta - del . (a - I) . del + b . del, -Delta - (a - I) . del(2) + b . del, where the second-order perturbations are given by the matrix a - I = c vertical bar x vertical bar(-2)x circle times x, c > -1. The vector field b : R-d -> R-d is form-bounded with form-bound delta > 0. (This includes vector fields with entries in L-d, as well as vector fields having critical-order singularities.) We characterize quantitative dependence on c and delta of the L-q -> W-1,W-qd/(d-2) regularity of solutions of the corresponding elliptic and parabolic equations in L-q, q >= 2 boolean OR (d - 2).
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收藏
页数:33
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