相关论文: Regularization of Ill-Posed Problems with Unbounde…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
In this paper we give and prove a criterion for the normality of unbounded closed operators, which is a sort of a maximality result which will be called "double maximality". As applications, we show, under some assumptions, that the sum of…
The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains $\Omega$ of $\mathbb{R}^d$. Our estimates are consistent with…
The main goal of this paper is to present the application of a superiorization methodology to solution of variational inequalities. Within this framework a variational inequality operator is considered as a small perturbation of a convex…
Variational inequalities with thin obstacles and Signorini-type boundary conditions are classical problems in the calculus of variations, arising in numerous applications. In the linear case many refined results are known, while in the…
We derive the solvability and regularity of the Dirichlet problem for fully non-linear elliptic equations possibly with degenerate right-hand side on Hermitian manifolds, through establishing a quantitative version of boundary estimate…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
We consider abstract operator equations $Fu=y$, where $F$ is a compact linear operator between Hilbert spaces $U$ and $V$, which are function spaces on \emph{closed, finite dimensional Riemannian manifolds}, respectively. This setting is of…
We consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
We generalize the classical K\"onig's and B\"ottcher's Theorems in complex dynamics to certain quasiregular mappings in the plane. Our approach to these results is unified in the sense that it does not depend on the local injectivity, or…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
In the present paper, we study the existence of normalized solutions for a Choquard type equation involving mixed diffusion type operators. We also provide regularity results of these solutions. Next, the equivalence between existence of…