Related papers: On Maximal Regularity for a Class of Evolutionary …
In this paper we derive for a controlled stochastic evolution system on a Hilbert space sufficient conditions for optimality. Our result is derived by using its so-called adjoint backward stochastic evolution equation.
We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…
This paper studies a maximal $L^q$-regularity property for nonlinear elliptic equations of second order with a zero-th order term and gradient nonlinearities having superlinear and sub-quadratic growth, complemented with Dirichlet boundary…
Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for a parabolic equation. We derive various stability results in…
We investigate the regularity of the strongly continuous semigroup associated with a system of two coupled second order evolution equations with indirect damping, whose stability was recently studied by Hao et al. By deriving the asymptotic…
We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
The nonlinear semigroup generated by the subdifferential of a convex lower semicontinuous function $\varphi$ has a smoothing effect, discovered by H. Br\'ezis, which implies maximal regularity for the evolution equation. We use this and…
In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…
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…
We study regularity properties of solutions to nonlinear and nonlocal evolution problems driven by the so-called \emph{$0$-order fractional $p-$Laplacian} type operators: $$ \partial_t u(x,t)=\mathcal{J}_p u(x,t):=\int_{\mathbb{R}^n}…
Given an ideal of forms in an algebra (polynomial ring, tensor algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we consider the Hilbert series of the factor ring. We concentrate on the minimal Hilbert series, which is…
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally…
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 propose a comprehensive framework for solving constrained variational inequalities via various classes of evolution equations displaying multi-scale aspects. In an infinite-dimensional Hilbertian framework, the class of dynamical systems…
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…