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

Kinzebulatov, Damir

doi:https://doi.org/10.18910/66997

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

Kinzebulatov, Damir

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

アクセス数:74件（2025-07-15 13:41 集計）

固定URL: https://doi.org/10.18910/66997

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タイトル	FELLER EVOLUTION FAMILIES AND PARABOLIC EQUATIONS WITH FORM-BOUNDED VECTOR FIELDS
著者	著者名 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.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	54(3)
ページ	499-516
刊行年月	2017-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/66997
DOI	https://doi.org/10.18910/66997
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 54, Number 3 （2017-7）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2017, 54(3), p. 499-516
DC.title	FELLER EVOLUTION FAMILIES AND PARABOLIC EQUATIONS WITH FORM-BOUNDED VECTOR FIELDS
DC.creator	Kinzebulatov, Damir
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2017-07
DCTERMS.abstract	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.
DC.identifier	10.18910/66997
DC.format	66997
citation_title	FELLER EVOLUTION FAMILIES AND PARABOLIC EQUATIONS WITH FORM-BOUNDED VECTOR FIELDS
citation_author	Kinzebulatov, Damir
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2017-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	54
citation_issue	3
citation_firstpage	499
citation_lastpage	516
citation_public_url	https://hdl.handle.net/11094/66997
citation_doi_detail	10.18910/66997
citation_doi	https://doi.org/10.18910/66997

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

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