Weighted maximal Lq(Lp)-regularity theory for time-fractional diffusion-wave equations with variable coefficients

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dc.contributor.authorPark, Daehanko
dc.date.accessioned2023-03-06T05:00:56Z-
dc.date.available2023-03-06T05:00:56Z-
dc.date.created2023-03-06-
dc.date.issued2023-03-
dc.identifier.citationJOURNAL OF EVOLUTION EQUATIONS, v.23, no.1-
dc.identifier.issn1424-3199-
dc.identifier.urihttp://hdl.handle.net/10203/305460-
dc.description.abstractWe 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.languageEnglish-
dc.publisherSPRINGER BASEL AG-
dc.titleWeighted maximal Lq(Lp)-regularity theory for time-fractional diffusion-wave equations with variable coefficients-
dc.typeArticle-
dc.identifier.wosid000926502100001-
dc.identifier.scopusid2-s2.0-85145443027-
dc.type.rimsART-
dc.citation.volume23-
dc.citation.issue1-
dc.citation.publicationnameJOURNAL OF EVOLUTION EQUATIONS-
dc.identifier.doi10.1007/s00028-022-00866-8-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorFractional diffusion-wave equation-
dc.subject.keywordAuthorLq(L p)-regularity theory-
dc.subject.keywordAuthorMuckenhoupt Ap weights-
dc.subject.keywordAuthorEquations with variable coefficients-
dc.subject.keywordAuthorCaputo fractional derivative-
dc.subject.keywordAuthorComplex interpolation of weighted Sobolev spaces-
dc.subject.keywordPlusSOBOLEV SPACES-
dc.subject.keywordPlusL-P-
dc.subject.keywordPlusANOMALOUS DIFFUSION-
dc.subject.keywordPlusPARABOLIC EQUATIONS-
dc.subject.keywordPlusINTERPOLATION-
dc.subject.keywordPlusINEQUALITIES-
dc.subject.keywordPlusREGULARITY-
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