Related papers: Remarks on maximal regularity

In this Short Note we complement the intriguing harmonic analytic perspective due to P. Auscher and A. Axelsson for the abstract evolution equations. This concerns a unified approach to temporally weighted estimates for the forward and…

In this work, we extend the Da Prato-Grisvard theory of maximal regularity estimates for sectorial operators in interpolation spaces. Specifically, for any generator $-A$ of an analytic semigroup on a Banach space $X$, we identify the…

We investigate the regularity in $L^p$ ($p>2$) of the gradient of any weak solution of a Cauchy problem with mixed Neumann-power type boundary conditions. Under suitable assumptions we prove the existence of weak solutions that satisfy…

In this paper we explore the theory of fractional powers of maximal accretive operators to obtain results of existence, regularity and behavior asymptotic of solutions for linear abstract evolution equations of third order in time.

We study maximal regularity in interpolation spaces for the sum of three closed linear operators on a Banach space, and we apply the abstract results to obtain Besov and H\"older maximal regularity for complete second order Cauchy problems…

We prove two maximal regularity results in spaces of continuous and H\"older continuous functions, for a mixed linear Cauchy-Dirichlet problem with a fractional time derivative $\mathbb{D}_t^\alpha$. This derivative is intended in the sense…

A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is…

In this work, we consider the Cauchy problem for $u' - Au = f$ with $A$ the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of…

We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $\Omega$ $\subseteq$ R n. We obtain maximal regularity in L 2…

We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of…

We study Cauchy problems associated to elliptic operators acting on vector-valued functions and coupled up to the first-order. We prove pointwise estimates for the spatial derivatives of the semigroup associated to these problems in the…

Recently, Auscher and Axelsson gave a new approach to non-smooth boundary value problems with $L^{2}$ data, that relies on some appropriate weighted maximal regularity estimates. As part of the development of the corresponding $L^{p}$…

We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with $L_2$ boundary data. The coefficients $A$ may depend on all variables, but are assumed to be close to…

In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…

The aim of this paper is to propose weak assumptions to prove maximal L^q regularity for Cauchy problem: du/dt - Lu(t)=f(t). Mainly we only require "off-diagonal" estimates on the real semigroup (e^{tL})_{t>0} to obtain maximal L^q…

We consider a non-autonomous Cauchy problem involving linear operators associated with time-dependent forms $a(t;.,.):V\times V\to {\mathbb{C}}$ where $V$ and $H$ are Hilbert spaces such that $V$ is continuously embedded in $H$. We prove…

In this paper, we investigate the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cut-off. We only deal with the physical case of hard potentials type interactions (with a…

We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…

For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…

This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit…