Results 311 to 320 of about 6,406,771 (368)
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1998
The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
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The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
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2014
The stochastic maximum principle (SMP) gives some necessary conditions for optimality for a stochastic optimal control problem. We give a summary of well-known results concerning stochastic maximum principle in finite-dimensional state space as well as some recent developments in infinite-dimensional state space.
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The stochastic maximum principle (SMP) gives some necessary conditions for optimality for a stochastic optimal control problem. We give a summary of well-known results concerning stochastic maximum principle in finite-dimensional state space as well as some recent developments in infinite-dimensional state space.
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2008
The maximum principle is formulated and proved first for control problems with fixed terminal time. As an illustration, a new derivation of the solution to the linear regulator problem is given. Next the maximum principle for impulse control problems and for time optimal problems are discussed.
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The maximum principle is formulated and proved first for control problems with fixed terminal time. As an illustration, a new derivation of the solution to the linear regulator problem is given. Next the maximum principle for impulse control problems and for time optimal problems are discussed.
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Maximum and Comparison Principles [PDF]
, 1977 The purpose of this chapter is to provide various maximum and comparison principles for quasilinear equations which extend corresponding results in Chapter 3. We consider second order, quasilinear operators Q of the form (10.1) Qu = aij(x, u, Du)Diju + b(x, u, Du), aij = aji, where x = (x1..., xn) is contained in a domain Ω of ℝn, n ≥ 2, and, unless ...
David Gilbarg, Neil S. Trudinger
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2001
We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
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We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
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2007
We consider classical linear and quasilinear elliptic inequalities as well as divergence structure and variational operators, with emphasis on the important topics of comparison results and tangency theorems. This work ultimately applies also to weak solutions in appropriate Sobolev spaces. In order that the book may serve the purposes of reference and
PUCCI, Patrizia, J. SERRIN
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We consider classical linear and quasilinear elliptic inequalities as well as divergence structure and variational operators, with emphasis on the important topics of comparison results and tangency theorems. This work ultimately applies also to weak solutions in appropriate Sobolev spaces. In order that the book may serve the purposes of reference and
PUCCI, Patrizia, J. SERRIN
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On the strong maximum principle
Complex Variables and Elliptic Equations, 2019In this paper we study the strong maximum principle for equations of the form F[u]=H(u,|Du|) where F is either a fully nonlinear elliptic operator or is the p-Laplace operator.
Ahmed Mohammed, Antonio Vitolo
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, 2015
The strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations.
Yikan Liu, W. Rundell, Masahiro Yamamoto
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The strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations.
Yikan Liu, W. Rundell, Masahiro Yamamoto
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The Pontryagin Maximum Principle for Nonlinear Optimal Control Problems with Infinite Horizon
Journal of Optimization Theory and Applications, 2015The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories.
Nico Tauchnitz
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