Trace regularity for biharmonic evolution equations with Caputo derivatives

Regularity of the Solutions for Nonlinear Biharmonic Equations in R

The purpose of this paper is to establish the regularity the weak solutions for the nonlinear biharmonic equation { ∆2u + a(x)u = g(x, u), u ∈ H2(RN ), where the condition u ∈ H2(RN ) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.

Maximal Regularity for Evolution Equations

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

Maximal regularity for nonautonomous evolution equations

We derive sufficient conditions, perturbation theorems in particular, for nonautonomous evolution equations to possess the property of maximal Lp regularity. 1991 Mathematics Subject Classification. 35K90, 47D06.

Maximal L-regularity for Stochastic Evolution Equations

We prove maximal Lp-regularity for the stochastic evolution equation{ dU(t) +AU(t) dt = F (t, U(t)) dt+B(t, U(t)) dWH(t), t ∈ [0, T ], U(0) = u0, under the assumption that A is a sectorial operator with a bounded H∞calculus of angle less than 1 2 π on a space Lq(O, μ). The driving process WH is a cylindrical Brownian motion in an abstract Hilbert space H. For p ∈ (2,∞) and q ∈ [2,∞) and initial...