An Lp -maximal regularity estimate of moments of solutions to second-order stochastic partial differential equations
DC Field | Value | Language |
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dc.contributor.author | Kim, I. | - |
dc.date.accessioned | 2022-03-03T10:40:47Z | - |
dc.date.available | 2022-03-03T10:40:47Z | - |
dc.date.created | 2022-02-09 | - |
dc.date.issued | 2022-03 | - |
dc.identifier.issn | 2194-0401 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/137612 | - |
dc.description.abstract | We obtain uniqueness and existence of a solution u to the following second-order stochastic partial differential equation: du=(a¯ij(ω,t)uxixj+f)dt+gkdwtk,t∈(0,T);u(0,·)=0,where T∈ (0 , ∞) , wk(k= 1 , 2 , …) are independent Wiener processes, (a¯ ij(ω, t)) is a (predictable) nonnegative symmetric matrix valued stochastic process such that κ|ξ|2≤a¯ij(ω,t)ξiξj≤K|ξ|2∀(ω,t,ξ)∈Ω×(0,T)×Rdfor some κ, K∈ (0 , ∞) , f∈Lp((0,T)×Rd,dt×dx;Lr(Ω,F,dP)),and g,gx∈Lp((0,T)×Rd,dt×dx;Lr(Ω,F,dP;l2))with 2 ≤ r≤ p< ∞ and appropriate measurable conditions. Moreover, for the solution u, we obtain the following maximal regularity moment estimate ∫0T∫Rd(E[|u(t,x)|r])p/rdxdt+∫0T∫Rd(E[|uxx(t,x)|r])p/rdxdt≤N(∫0T∫Rd(E[|f(t,x)|r])p/rdxdt+∫0T∫Rd(E[|g(t,x)|l2r])p/rdxdt+∫0T∫Rd(E[|gx(t,x)|l2r])p/rdxdt),where N is a positive constant depending only on d, p, r, κ, K, and T. As an application, for the solution u to (1), the rth moment mr(t, x) : = E| u(t, x) | r is in the parabolic Sobolev space Wp/r1,2((0,T)×Rd). © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | Springer | - |
dc.title | An Lp -maximal regularity estimate of moments of solutions to second-order stochastic partial differential equations | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, I. | - |
dc.identifier.doi | 10.1007/s40072-021-00201-1 | - |
dc.identifier.scopusid | 2-s2.0-85107805227 | - |
dc.identifier.wosid | 000660801200001 | - |
dc.identifier.bibliographicCitation | Stochastics and Partial Differential Equations: Analysis and Computations, v.10, no.1, pp.278 - 316 | - |
dc.relation.isPartOf | Stochastics and Partial Differential Equations: Analysis and Computations | - |
dc.citation.title | Stochastics and Partial Differential Equations: Analysis and Computations | - |
dc.citation.volume | 10 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 278 | - |
dc.citation.endPage | 316 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.subject.keywordPlus | SOBOLEV SPACE THEORY | - |
dc.subject.keywordPlus | PSEUDODIFFERENTIAL-OPERATORS | - |
dc.subject.keywordPlus | SPDES | - |
dc.subject.keywordPlus | COEFFICIENTS | - |
dc.subject.keywordPlus | DRIVEN | - |
dc.subject.keywordAuthor | Maximal regularity moment estimate | - |
dc.subject.keywordAuthor | Stochastic partial differential equations | - |
dc.subject.keywordAuthor | Zero initial evolution equation | - |
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