About smoothness of solutions of the heat equations in closed, smooth space‐time domains | Zendy

Dong Hongjie | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

About smoothness of solutions of the heat equations in closed, smooth space‐time domains

Author(s) -

Dong Hongjie

Publication year - 2005

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.20079

Subject(s) - smoothness , mathematics , heat equation , bounded function , domain (mathematical analysis) , order (exchange) , boundary (topology) , mathematical analysis , class (philosophy) , space (punctuation) , probabilistic logic , pure mathematics , combinatorics , linguistics , philosophy , statistics , finance , artificial intelligence , computer science , economics

We consider the probabilistic solutions of the heat equation u x 2= u x 1 x 1+ f in D , where D is a bounded domain in ℝ 2 = {( x 1 , x 2 )} of class C 2 k . We give sufficient conditions for u to have k th ‐order continuous derivatives with respect to ( x 1 , x 2 ) in D̄ for integers k ≥ 2. The equation is supplemented with C 2 k boundary data, and we assume that f ϵ C 2( k −1) . We also prove that our conditions are sharp by examples in the border cases. © 2005 Wiley Periodicals, Inc.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research