Related papers: Vectorial Double Phase Obstacle Problems
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
An important concept of convexificators has been extended to Hadamard manifolds in this paper. The mean value theorem for convexificators on the Hadamard manifold has also been derived. Monotonicity of the bounded convexificators has been…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
We study the connection between a multitime scalar variational problem (SVP), a multitime vector variational problem (VVP) and a multitime vector fractional variational problem (VFP). For (SVP), we establish necessary optimality conditions.…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
We study the minimizers of the fusion frame potential in the case that both the weights and the dimensions of the subspaces are fixed and not necessarily equal. Using a concept of irregularity we provide a description of the local (that are…
We prove the partial H\"older continuity on boundary points for minimizers of quasiconvex non-degenerate functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\mathrm{d}x, \end{equation*} where $f$…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
We investigate the De Giorgi-Nash-Moser theory for minimizers of mixed local and nonlocal functionals modeled after \[ v \mapsto…
We prove optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.
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…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if this repulsion is like Newtonian or more singular than…
Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints. In this paper, we theoretically…
This paper is devoted to presenting new interior regularity criteria in terms of one velocity component for weak solutions to the Navier-Stokes equations in three dimensions. It is shown that the velocity is regular near a point $z$ if its…
We establish general assumptions under which a constrained vari- ational problem involving the fractional gradient and a local nonlin- earity admits minimizers.
We establish the higher differentiability of solutions to a class of obstacle problems for integral functionals where the convex integrand f satisfies p-growth conditions with respect to the gradient variable. We derive that the higher…
In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension. In particular, we study almost fractional harmonic…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We prove partial regularity for minimizers of quasiconvex functionals of the type $\int_\Omega f(x,Du) dx$ with $p(x)$ growth with respect to the second variable. The proof is direct and uses a method of $A$-harmonic approximation.