A note on Banach spaces and sub differentials of convex functions
A note on boundary value problems for second order differential equations
A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory
The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower...
A note on convergence of level sets.
A Note on Embeddings for the Augmented Lagrange Method
A note on equality of functional envelopes
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in , , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.
A Note on Exterior Capillarity Problems.
A note on Minty type vector variational inequalities
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are introduced....
A note on Minty type vector variational inequalities
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced. Under...
A note on necessary conditions in mathematical programming
A note on quasiconvexity and rank-one convexity for matrices.
A note on quasi-monotone operators.
A note on Ricci flow and optimal transportation
We describe a new link between Perelman’s monotonicity formula for the reduced volume and ideas from optimal transport theory.
A note on singular points of convex functions in Banach spaces
A note on the characterization of the global maxima of a (tangentially) convex function over a convex set.
A note on the closedness of the convex hull and its applications.
A Note on the Interpretation of Closed H-Surfaces in Physical Terms.
A note on the optimal portfolio problem in discrete processes
We deal with the optimal portfolio problem in discrete-time setting. Employing the discrete Itô formula, which is developed by Fujita, we establish the discrete Hamilton–Jacobi–Bellman (d-HJB) equation for the value function. Simple examples of the d-HJB equation are also discussed.
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the hamiltonian. The proof relies on a reverse Hölder inequality.
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.