10 research outputs found
Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints
In this paper, we consider non-diffusive variational problems with mixed
boundary conditions and (distributional and weak) gradient constraints. The
upper bound in the constraint is either a function or a Borel measure, leading
to the state space being a Sobolev one or the space of functions of bounded
variation. We address existence and uniqueness of the model under low
regularity assumptions, and rigorously identify its Fenchel pre-dual problem.
The latter in some cases is posed on a non-standard space of Borel measures
with square integrable divergences. We also establish existence and uniqueness
of solutions to this pre-dual problem under some assumptions. We conclude the
paper by introducing a mixed finite-element method to solve the primal-dual
system. The numerical examples confirm our theoretical findings
LIPSCHITZ CONTINUITY FOR ENERGY INTEGRALS WITH VARIABLE EXPONENTS
A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set WHRn, with variable exponent p(x) in the Sobolev class W1; r loc W for some r > n, is locally Lipschitz continuous in W and an a priori estimate holds
Entropy solutions for nonlinear elliptic anisotropic problem with Robin boundary condition
We study a Robin boundary value problem of nonlinear elliptic anisotropic type. We prove the existence and uniqueness of entropy solutions for -data, via the existence and uniqueness of weak solution
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described