FELLER EVOLUTION FAMILIES AND PARABOLIC EQUATIONS WITH FORM-BOUNDED VECTOR FIELDS

• Kinzebulatov Damir

抄録

e show that the weak solutions of parabolic equation ∂ₜu − Δu + b(t, x) · ∇u = 0, (t, x) ∈ (0,∞) × ℝ^d, d?≽ 3, for b(t,x) in a wide class of time-dependent vector fields capturing critical order singularities, constitute a Feller evolution family and, thus, determine a Feller process. Our proof uses an a priori estimate on the L^p-norm of the gradient of solution in terms of the L^q-norm of the gradient of initial function, and an iterative procedure that moves the problem of convergence in L^∞ to L^p.

収録刊行物

• Osaka Journal of Mathematics

  Osaka Journal of Mathematics 54 (3), 499-516, 2017-07

  Osaka University and Osaka City University, Departments of Mathematics

詳細情報

• CRID: 1390572174764034432
• NII論文ID: 120006336195
• NII書誌ID: AA00765910
• DOI: 10.18910/66997
• HANDLE: 11094/66997
• ISSN: 00306126
• Web Site: https://dlisv03.media.osaka-cu.ac.jp/il/meta_pub/G0000438repository_111F0000002-05403-05
• 本文言語コード: en
• データソース種別:
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  • IRDB
  • CiNii Articles