Results 251 to 260 of about 1,011,292 (311)
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A Free Boundary Optimization Problem
SIAM Journal on Mathematical Analysis, 1978Given a convex set $Q \subset R^2 $ (bounded by a simple closed curve) and a constant $A > 0$, we determine the doubly-connected region $\Omega $ encircling (but not intersecting) Q, with area $| \Omega | \leqq A$, which has the least capacitance.
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On the fine structure of the free boundary for the classical obstacle problem
Inventiones Mathematicae, 2017In the classical obstacle problem, the free boundary can be decomposed into “regular” and “singular” points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139:155–184, 1977; J Fourier Anal Appl 4:383–402, 1998), regular points ...
A. Figalli, J. Serra
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A free boundary problem related to thermal insulation
, 2015We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but rather a ...
L. Caffarelli, D. Kriventsov
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Izvestiya: Mathematics, 2002
This paper deals with the regularity properties of solutions for the double nonlinear parabolic equation \[ u_t-D\left(u^{p_0}Du+| Du| ^{p_1}Du \right)=f(x,t). \tag{1} \] A Stefan-like problem for the one-dimensional analogue of equation (1) is also considered.
Soltanov, K. N., Novruzov, E. B.
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This paper deals with the regularity properties of solutions for the double nonlinear parabolic equation \[ u_t-D\left(u^{p_0}Du+| Du| ^{p_1}Du \right)=f(x,t). \tag{1} \] A Stefan-like problem for the one-dimensional analogue of equation (1) is also considered.
Soltanov, K. N., Novruzov, E. B.
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2013
As we know, a problem of pricing an American-style derivative can be formulated as a linear complementarity problem, and for most cases, it can also be written as a free-boundary problem. In Chap. 8, we have discussed how to solve a linear complementarity problem. Here, we study how to solve a free-boundary problem numerically. Many derivative security
You-lan Zhu +3 more
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As we know, a problem of pricing an American-style derivative can be formulated as a linear complementarity problem, and for most cases, it can also be written as a free-boundary problem. In Chap. 8, we have discussed how to solve a linear complementarity problem. Here, we study how to solve a free-boundary problem numerically. Many derivative security
You-lan Zhu +3 more
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Nonlinear Analysis: Theory, Methods & Applications, 2008
We are concerned with the existence of positive solutions of the following discontinuous problem: \[ -\Delta u=f(u)H(u-\mu)\quad\text{in }\Omega, \qquad u=h\quad\text{on }\partial\Omega, \] where \(\Omega\) is the unit ball of \(\mathbb R^n\) \((n\geq 3)\) and \(H\)H is the Heaviside function.
Bensid, Sabri, Bouguima, S. M.
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We are concerned with the existence of positive solutions of the following discontinuous problem: \[ -\Delta u=f(u)H(u-\mu)\quad\text{in }\Omega, \qquad u=h\quad\text{on }\partial\Omega, \] where \(\Omega\) is the unit ball of \(\mathbb R^n\) \((n\geq 3)\) and \(H\)H is the Heaviside function.
Bensid, Sabri, Bouguima, S. M.
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On the Measure and the Structure of the Free Boundary of the Lower Dimensional Obstacle Problem
, 2017We provide a thorough description of the free boundary for the lower dimensional obstacle problem in $${\mathbb{R}^{n+1}}$$Rn+1 up to sets of null $${\mathcal{H}^{n-1}}$$Hn-1 measure.
M. Focardi, Emanuele Spadaro
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1983
One example of a flow with a free boundary is that of a jet of fluid travelling through a region of constant pressure. There are two typical situations which are shown in Figure. The first is a jet impinging on a fixed wall and the second is a jet emerging from a hole in the wall of a large reservoir.
Hilary Ockendon, Alan B. Tayler
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One example of a flow with a free boundary is that of a jet of fluid travelling through a region of constant pressure. There are two typical situations which are shown in Figure. The first is a jet impinging on a fixed wall and the second is a jet emerging from a hole in the wall of a large reservoir.
Hilary Ockendon, Alan B. Tayler
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2017
Obstacle and contact problems leading to variational inequalities as well as models for porous media are studied. A main theme is phase transitions appearing in the context of solidification processes. Finally, also free boundary problems in fluid dynamics are considered.
Christof Eck +2 more
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Obstacle and contact problems leading to variational inequalities as well as models for porous media are studied. A main theme is phase transitions appearing in the context of solidification processes. Finally, also free boundary problems in fluid dynamics are considered.
Christof Eck +2 more
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On One Nonlocal Problem with Free Boundary
Ukrainian Mathematical Journal, 2001The author considers the equation \( \frac{\partial^2 u}{\partial x^2} + \frac{n-1}{x} \frac{\partial u}{\partial x} - g(u) \frac{\partial u} {\partial t}=0\), \(x,t\in{\mathbb R}_+^1\), \(n=1,2,3.\) The function \( g(u)\), \(u>0\) is positive, continuous, decreasing and has integrable singularity at the point \(u=0.\) By means of the functional \( f(u)
Mitropol'skij, Yu. A. +2 more
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