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Aleksandrov maximum principle and bony maximum principle for parabolic equations
Acta Mathematicae Applicatae Sinica, 1985The author simplifies the proof of the Aleksandrov maximum principle for parabolic equations given by Krylov and obtains finer results. He further proves the Bony maximum principle for parabolic equations by using the above results.
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The Classical Maximum Principle
1977The purpose of this chapter is to extend the classical maximum principles for the Laplace operator, derived in Chapter 2, to linear elliptic differential operators of the form $$Lu \equiv {a^{ij}}\left( x \right){D_{ij}}u + {b^i}\left( x \right){D_i}u + c\left( x \right)u,\quad {a^{ij}} = {a^{ji}},$$ (3.1) where x = (x 1, … , x n ) lies in a ...
David Gilbarg, Neil S. Trudinger
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Maximum Principles for Nonlinear Fractional Differential Equations in Reliable Space
Progress in Fractional Differentiation and Applications, 2020semanticscholar +1 more source
Maximum Principles for k-Hessian Equations with Lower Order Terms on Unbounded Domains
Journal of Geometric Analysis, 2020T. Bhattacharya, Ahmed Mohammed
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Maximum principles for some quasilinear elliptic systems
Nonlinear Analysis, 2020S. Leonardi +4 more
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1992
Publisher Summary This chapter describes the yield and procedure of maximum principles. It is applicable to linear ordinary differential equations, and linear partial differential equations. It yields upper, or lower bounds on the solution. By the use of a maximum theorem, one can find bounds on certain types of equations.
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Publisher Summary This chapter describes the yield and procedure of maximum principles. It is applicable to linear ordinary differential equations, and linear partial differential equations. It yields upper, or lower bounds on the solution. By the use of a maximum theorem, one can find bounds on certain types of equations.
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Pontriagin's maximum principle and the principle of optimality
Journal of the Franklin Institute, 1961Abstract This paper demonstrates that Pontriagin's Maximum Principle may be derived from the principle of Optimality. It considers a control system described by ẋ = f(x, u, t) where the control vector u is restricted to a closed and bounded set. The optimal control steers the system from an initial state x0 at 0 to a moving target in such a way that ...
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Maximum principles in differential equations
, 1967M. Protter, H. Weinberger
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