Variational Principles and Convergence of Finite Element Approximations of a Holonomic Elastic-Plastic Problem.
Variational Principles for Monotone and Maximal Bifunctions
2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.
Variational principles for set-valued mappings with applications to multiobjective optimization
Variational problems on classes of rearrangements and multiple configurations for steady vortices
Variational problems with free boundaries for the fractional Laplacian
We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.
Variational problems with lipschitzian minimizers
Variational problems with moving boundaries using decomposition method.
Variational problems with non-constant gradient constraints.
Variational Problems with Non-Convex Obstacles an and Integral-Constraint for Vector-Valued Functions.
Variational solutions of stationary Hamilton-Jacobi equations.
Variational stability and well-posedness in the optimal control of ordinary differential equations
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Variational-like inclusions and resolvent equations involving infinite family of set-valued mappings.
Variationsprobleme mehrfacher Integrale mit symmetrischer Transversalitätsbedingung.
Vector and operator valued measures as controls for infinite dimensional systems: optimal control
In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear...
Vector Optimization Results for -Stable Data
The aim of this paper is to summarize basic facts about -stable at a point vector functions and existing results for certain vector constrained programming problem with -stable data.
Vector variational problems and applications to optimal design
We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical...
Vector variational problems and applications to optimal design
We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical...
Vectorial form of Ekeland-type variational principle in locally convex spaces and its applications.
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.