Nonautonomous maximal Lp-regularity under fractional Sobolev regularity in time
Copyright policy )Nonautonomous maximal Lp-regularity under fractional Sobolev regularity in time
We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H��lder assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In particular, on $L^q(��)$ we obtain maximal $L^p$-regularity for $p \ge 2$ and elliptic operators in divergence form with uniform $VMO$-modulus in space and $W^{��,p}$-regularity for $��> \frac{1}{2}$ in time.
19 pages
- University of Ulm Germany
Quasilinear parabolic equations, 35B65, One-parameter semigroups and linear evolution equations, Smoothness and regularity of solutions to PDEs, parabolic equations in divergence form, 35K10, quasilinear parabolic problems, 35B45, A priori estimates in context of PDEs, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, nonautonomous maximal regularity, FOS: Mathematics, 47D06, 35B65 (Primary) 35K10, 35B45, 47D06 (Secondary), \(L^p\)-regularity results on UMD spaces, Analysis of PDEs (math.AP)
Quasilinear parabolic equations, 35B65, One-parameter semigroups and linear evolution equations, Smoothness and regularity of solutions to PDEs, parabolic equations in divergence form, 35K10, quasilinear parabolic problems, 35B45, A priori estimates in context of PDEs, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, nonautonomous maximal regularity, FOS: Mathematics, 47D06, 35B65 (Primary) 35K10, 35B45, 47D06 (Secondary), \(L^p\)-regularity results on UMD spaces, Analysis of PDEs (math.AP)
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