Page 1 Next

## Displaying 1 – 20 of 80

Showing per page

### A differential inclusion : the case of an isotropic set

ESAIM: Control, Optimisation and Calculus of Variations

In this article we are interested in the following problem: to find a map $u:\Omega \to {ℝ}^{2}$ that satisfies$\left\{\begin{array}{cc}Du\in E\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\hfill & \mathit{\text{a.e.}}\phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}\Omega \hfill \\ u\left(x\right)=\varphi \left(x\right)\hfill & x\in \partial \Omega \phantom{\rule{85.35826pt}{0ex}}\hfill \end{array}\right\$where $\Omega$ is an open set of ${ℝ}^{2}$ and $E$ is a compact isotropic set of ${ℝ}^{2×2}$. We will show an existence theorem under suitable hypotheses on $\varphi$.

### A differential inclusion: the case of an isotropic set

ESAIM: Control, Optimisation and Calculus of Variations

In this article we are interested in the following problem: to find a map $u:\Omega \to {ℝ}^{2}$ that satisfies $\left\{\begin{array}{cc}Du\in E\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\hfill & \mathit{\text{a.e.}}\phantom{\rule{4.0pt}{0ex}}\text{in}\phantom{\rule{4.0pt}{0ex}}\Omega \hfill \\ u\left(x\right)=\varphi \left(x\right)\hfill & x\in \partial \Omega \hfill \end{array}\right\$ where Ω is an open set of ${ℝ}^{2}$ and E is a compact isotropic set of ${ℝ}^{2×2}$. We will show an existence theorem under suitable hypotheses on φ.

### A Helly number for unions of two boxes in ${ℝ}^{2}$.

International Journal of Mathematics and Mathematical Sciences

### A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.

Discrete &amp; computational geometry

### A note on Kakutani Lemma

Matematički Vesnik

### A simple geometrie proof of a theorem for starshaped unions of convex sets

Acta Universitatis Carolinae. Mathematica et Physica

### A staircase illumination theorem for orthogonal polygons.

Beiträge zur Algebra und Geometrie

### A unified treatment of the theories of matroids with coefficients and of $\text{Δ}$-matroids with coefficients.

Beiträge zur Algebra und Geometrie

### Ambiguous Loci of the Metric Projection Onto Compact Starshaped Sets in a Banach Space.

Monatshefte für Mathematik

### An analogue of the Krein-Milman theorem for star-shaped sets.

Beiträge zur Algebra und Geometrie

### Approximation of symmetric convex bodies.

Extracta Mathematicae

### Camera Placement in Integer Lattices.

Discrete &amp; computational geometry

### Characterizing certain staircase convex sets in ${ℝ}^{d}$.

Beiträge zur Algebra und Geometrie

### Choquet theory in metric spaces.

Zeitschrift für Analysis und ihre Anwendungen

### Concerning Sets of the First Baire Category with Respect to Different Metrics

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that if ${\varrho }_{H}$ and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to ${\varrho }_{H}$ need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.

### Conformal Mappings onto Prescribed Regions via Optimization Techniques.

Numerische Mathematik

### Continuity of the visibility function.

Publicacions Matemàtiques

G. Beer defined the visibility function of a set S and proved its continuity in the interior of S. It is proved here that the visibility function of a planar Jordan domain is continuous precisely at the cone points of the boundary of S.

### Cooperative guards in art galleries with one hole.

Balkan Journal of Geometry and its Applications (BJGA)

### Covering belt bodies by smaller homothetical copies.

Beiträge zur Algebra und Geometrie

### Determining Dimension of the Kernel of a Cone.

Monatshefte für Mathematik

Page 1 Next