DC Field | Value | Language |
---|---|---|
dc.contributor.author | Park, Daehan | ko |
dc.date.accessioned | 2023-03-06T05:00:56Z | - |
dc.date.available | 2023-03-06T05:00:56Z | - |
dc.date.created | 2023-03-06 | - |
dc.date.issued | 2023-03 | - |
dc.identifier.citation | JOURNAL OF EVOLUTION EQUATIONS, v.23, no.1 | - |
dc.identifier.issn | 1424-3199 | - |
dc.identifier.uri | http://hdl.handle.net/10203/305460 | - |
dc.description.abstract | We present a maximal Lq(L p)-regularity theory with Muckenhoupt weights for the equation & part;(alpha)(t)u(t,x)=a(ij)(t,x)u (x)i(x)j(t,x)+f(t,x), t > 0, x is an element of R-d. (0.1)Here, & part;(alpha )(t)is the Caputo fractional derivative of order alpha is an element of(0, 2) and aijare functions of (t,x). Precisely, we show that integral (T)( 0) (integral(d)(R)|(1 - delta)gamma/2(u)xx(t, x)|pw(1)(x)dx) w2(t)dt <= N integral( T)(0) (integral(d)(R) |(1 - delta)gamma/2 f (t, x)|pw1(x)dx w2(t)dt, 0where 1 < p, q < infinity, gamma is an element of R, and w1 and w2 are Muckenhoupt weights. This implies that we prove maximal regularity theory, and sharp regularity of solution according to regularity of f . To prove our main result, we also proved the complex interpolation of weighted Sobolev spaces,[H-p0(gamma 0)(w0), H-p1(gamma 1) (w(1))][theta] =H-p(gamma)(w), where theta is an element of (0, 1), gamma 0, gamma 1 is an element of R, p0, p1 is an element of (1, infinity), wi (i = 0, 1) are arbitrary A(pi )weight, and gamma = (1 - theta)gamma 0 + theta gamma 1, 1 /p 1 - theta = /p0 + theta , w(1)/p = w p1 (1-theta) 0 w/ p0 theta 1 . p1 | - |
dc.language | English | - |
dc.publisher | SPRINGER BASEL AG | - |
dc.title | Weighted maximal Lq(Lp)-regularity theory for time-fractional diffusion-wave equations with variable coefficients | - |
dc.type | Article | - |
dc.identifier.wosid | 000926502100001 | - |
dc.identifier.scopusid | 2-s2.0-85145443027 | - |
dc.type.rims | ART | - |
dc.citation.volume | 23 | - |
dc.citation.issue | 1 | - |
dc.citation.publicationname | JOURNAL OF EVOLUTION EQUATIONS | - |
dc.identifier.doi | 10.1007/s00028-022-00866-8 | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Fractional diffusion-wave equation | - |
dc.subject.keywordAuthor | Lq(L p)-regularity theory | - |
dc.subject.keywordAuthor | Muckenhoupt Ap weights | - |
dc.subject.keywordAuthor | Equations with variable coefficients | - |
dc.subject.keywordAuthor | Caputo fractional derivative | - |
dc.subject.keywordAuthor | Complex interpolation of weighted Sobolev spaces | - |
dc.subject.keywordPlus | SOBOLEV SPACES | - |
dc.subject.keywordPlus | L-P | - |
dc.subject.keywordPlus | ANOMALOUS DIFFUSION | - |
dc.subject.keywordPlus | PARABOLIC EQUATIONS | - |
dc.subject.keywordPlus | INTERPOLATION | - |
dc.subject.keywordPlus | INEQUALITIES | - |
dc.subject.keywordPlus | REGULARITY | - |
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