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We prove maximal Lp-Lp a—priori estimates for the solution of the parabolic evolution equation u'(t)=Au(t)+f(t), u(0)=0 provided Tmay be represented by a heat—kernel satisfying certain bounds (and in particular a Gaussian bound). 1991 Mathematics Subject Classification:35K22, 58D25, 47D06","publishedDate","1997-01-01","publishedYear",1997,"venue","Communications in Partial Differential Equations",291,"authors","keywords",[183,184,185],"pdfUrl","topVenue","Advanced Mathematical Modeling in Engineering","Stability and Controllability of Differential Equations","Numerical methods in inverse problems","paper_W4234760113","ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type","{\"openalex\":\"W4234760113\",\"doi\":\"10.1090/memo/0788\"}","2026-05-20T13:47:22.201014775","2026-05-20T13:47:22.214695759","10.1090/memo/0788","W4234760113","2003-01-01",2003,"Memoirs of the American Mathematical Society",330,[198,199,183],"Differential Equations and Boundary Problems","advanced mathematical theories","paper_W2492922843","Moving Interfaces and Quasilinear Parabolic Evolution Equations","{\"openalex\":\"W2492922843\",\"doi\":\"10.1007/978-3-319-27698-4\"}","2026-05-20T01:29:20.192731202","2026-05-20T01:29:20.19510374","10.1007/978-3-319-27698-4","W2492922843","2016-01-01",2016,"Monographs in mathematics",364,[183,212,213],"Differential Equations and Numerical Methods","Nonlinear Partial Differential Equations","paper_W4236945040","On the Spectrum of C 0 -Semigroups","{\"openalex\":\"W4236945040\",\"doi\":\"10.2307/1999112\"}","2026-05-16T13:10:41.205402876","2026-05-19T06:21:39.195500503","10.2307/1999112","W4236945040","1984-08-01",1984,"Transactions of the American Mathematical Society",452,[226,227],"Functional Equations Stability Results","semigroups and automata theory","paper_W1495844786","On the spectrum of 𝐶₀-semigroups","{\"openalex\":\"W1495844786\",\"doi\":\"10.1090/s0002-9947-1984-0743749-9\"}","2026-05-16T07:44:53.189264217","2026-05-19T03:54:36.175133216","10.1090/s0002-9947-1984-0743749-9","W1495844786","In this paper we give characterizations of the spectrum of a C 0 {C_0} -semigroup e A t {e^{At}} in terms of certain solution properties of the differential equation ( ∗ ) u ′ = A u + f (\\ast )\\;u’ = Au + f and, in case X X is a Hilbert space, also in terms of properties of ( λ − A ) − 1 {(\\lambda - A)^{ - 1}} . We give several applications of these results including a study of the existence of dichotomic projections for ( ∗ ) (\\ast ) .","1984-01-01",477,[184,240,183],"https://www.ams.org/tran/1984-284-02/S0002-9947-1984-0743749-9/S0002-9947-1984-0743749-9.pdf","Nonlinear Differential Equations Analysis","paper_W2080666567","R-Boundedness, Fourier Multipliers, and Problems of Elliptic and Parabolic Type","{\"openalex\":\"W2080666567\"}","2026-05-15T05:29:53.197759785","2026-05-21T03:53:44.186196182","W2080666567","Introduction Notations and conventions $\\mathcal R$-Boundedness and Sectorial Operators: Sectorial operators The classes ${\\mathcal{BIP}}(X)$ and $\\mathcal H^\\infty(X)$ $\\mathcal R$-bounded families of operators $\\mathcal R$-sectorial operators and maximal $L_p$-regularity Elliptic and Parabolic Boundary Value Problems: Elliptic differential operators in $L_p(\\mathbb{R}^n E)$ Elliptic problems in a half space: General Banach spaces Elliptic problems in a half space: Banach spaces of class $\\mathcal{HT}$ Elliptic and parabolic problems in domains Notes 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Jan Prüß 人物

Jan Prüß · 相关文章