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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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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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2010
This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al.
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This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al.
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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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Symmetry and related properties via the maximum principle
, 1979B. Gidas, W. Ni, L. Nirenberg
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Information Theory and an Extension of the Maximum Likelihood Principle
, 1973H. Akaike
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1991
The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
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The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
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