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For a given domain $Ω \subset ℝ^{n}$ , we consider the variational problem of minimizing the $L^{1}$ -norm of the gradient on $Ω$ of a function $u$ with prescribed continuous boundary values and satisfying a continuous lower obstacle condition $u \geq ψ$ inside $Ω$ . Under the assumption of strictly positive mean curvature of the boundary $\partial Ω$ , we show existence of a continuous solution, with Holder exponent half of that of data and obstacle. This generalizes previous results obtained for the unconstrained and double-obstacle problems. The...

The Obstacle Problem Revisited.

L.A. Caffarelli (1998)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

The operation of infimal convolution [Book]

Strömberg Thomas (1996)

The optimal control chart procedure

Jaroslav Skřivánek (2004)

Kybernetika

The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span $k$ is specified by a partition of the space $ℝ^{k}$ into three disjoint parts. We call this partition as the control chart frame of span $k .$ A shift in the process parameter is signalled at time $t$ by having the vector of the last $k$ sample characteristics fall out of the...

The optimal shape of a dendrite sealed at both ends

Yannick Privat (2009)

Annales de l'I.H.P. Analyse non linéaire

The optimization of the stationary heat equation with a variable right-hand side

Ctirad Matyska (1986)

Aplikace matematiky

Solving the stationary heat equation we optimize the temperature on part of the boundary of the domain under investigation. First the Poisson equation is solved; both the Neumann condition on part of the boundary and the Newton condition on the rest are prescribed, the distribution of the heat sources being variable. In the second case, the heat equation also contains a convective term, the distribution of heat sources is specified and the Neumann condition is variable on part of the boundary.

The origin of variational principles

Włodzimierz M. Tulczyjew (2003)

Banach Center Publications

The $p$ -Laplace eigenvalue problem as $p \to \infty$ in a Finsler metric

M. Belloni, Bernhard Kawohl, P. Juutinen (2006)

Journal of the European Mathematical Society

We consider the $p$ -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite $p$ and investigate the limit problem as $p \to \infty$ .

The $p$ -Laplacian in domains with small random holes

M. Balzano, T. Durante (2003)

Bollettino dell'Unione Matematica Italiana

$P_{h}$ {ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . where $2 \leq p \leq n$ and $E_{h}$ are random subsets of a bounded open set $D$ of $R^{n}$ $(n \geq 2)$ . By...

The $p$ -Laplacian – mascot of nonlinear analysis.

Drábek, Pavel (2007)

Acta Mathematica Universitatis Comenianae. New Series

The $p$ -Laplacian – mascot of nonlinear analysis

Drábek, P. (2007)

Proceedings of Equadiff 11

The parametric Weierstrass integral over a BV curve as a length functional

Loris Faina (1998)

Studia Mathematica

The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.

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Displaying 101 – 120 of 272

The non-parameter penalty function method in constrained optimal control problems.

The nonsmooth maximum principle

The non-standard LQR problem for boundary control systems.

The nonzero solutions and multiple solutions for a class of bilinear variational inequalities.

The Numerical Solution of the Inverse Stefan Problem.

The obstacle problem for functions of least gradient