Calculus of Variations, Applications and Computations

This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.

PrefaceIsoperimetric Inequalities for a Generalized Multidimensional Muskat ProblemSolution of a Free Boundary Problem of the Hele-Shaw Type, in the Ovsjannikov ScalesContinuous Polarization and Symmetry of Solutions of Variational Problems with PotentialsAn Optimal Control Problem for a Nonlinear Elliptic Equation Arising from Population DynamicsGlobal existence of Functional Solutions for the Vlasov-Poisson-Fokker-Planck System in 3 D with Bounded Measures as Initial DataNumerical Methods for a Forward Backward Heat EquationOn a Dirichlet Problem Related to the Invertibility of Mappings Arising in 2D Grid GenerationOn Rank One Convex Functions Which are Homogeneous of Degree OneOn the Approximation of the Curve Shortening FlowFlows Through Saturated Mass Exchanging Porous Media Under High Pressure GradientsExistence of Nontrivial Solutions to the Marguerre-Von Karman Equations,Quasiconvex Envelopes of Stored Energy Densities that are Convex with Respect to the Strain TensorApplication of Quasi Steady Solutions of Soil Freezing for Geotechnical EngineeringCurvature Driven Interface MotionDiscretization of Second Order Elliptic Differential Equations on Sparse GridsHydrodynamic stability and a Posterior Error Control in the Solution of the Navier-Stokes EquationsPartial Regularity for Incompressible Materials with Approximation MethodsA Note About Relaxation of Vectorial Variational ProblemsNumerical Simulation of Boundary Layer Problem with SeparationMaximal Inequalities and Applications to Regularity Problems in the Calculus of VariationsCritical Points for Pairs of Functionals and Semilinear Elliptic EquationsFront Propagation in Diffusion Problems on TreesA Gamma Limit Approach for Viscosity Stationary Solutions of a Model Convection Equation