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Communications on Pure and Applied Mathematics, 1965
Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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Homogenization of Differential Operators
Acta Mathematicae Applicatae Sinica, English Series, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON SECOND ORDER DIFFERENTIAL OPERATORS
The Annals of Mathematics, 1955Nevertheless, (1.2) is meaningful only under differentiability conditions which are unnatural for (1.1). An adjoint to (1.1) exists always, but it cannot be written in terms of derivatives with respect to x. The characteristic property of A appears to be (1) that it is of local character, (2) that whenever f has a local minimum at xo and f(xo) = 0 ...
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DEGENERATING ELLIPTIC DIFFERENTIAL AND PSEUDO-DIFFERENTIAL OPERATORS
Russian Mathematical Surveys, 1970The present paper is a survey of some results concerning higher-order elliptic differential operators which degenerate on the boundary of a domain. The principal aspect in the study of such operators is that of investigating the corresponding ordinary equations with parameters which degenerate at a single point.
Vishik, M. I., Grushin, V. V.
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Differential Operators and Differential Modules
2003In this chapter k is a differential field such that its subfield of constants C is different from k and has characteristic 0. The skew (i.e., noncommutative) ring D :=k[∂] consists of all expressions L :=a n ∂ n + ⋯ + a1∂ + a0 dot with n ∈ Z, n ≥ 0 and all a i ∈ k. These elements L are called differential operators.
Marius van der Put, Michael F. Singer
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2003
This chapter is essentially a brief introduction to non-linear functional analysis. First, we define the Gâteaux and Frechet derivatives of generally non-linear operators between linear vector spaces and we investigate their properties in some considerable detail.
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This chapter is essentially a brief introduction to non-linear functional analysis. First, we define the Gâteaux and Frechet derivatives of generally non-linear operators between linear vector spaces and we investigate their properties in some considerable detail.
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A new selection operator for differential evolution algorithm
Knowledge-Based Systems, 2021Zhiqiang Zeng, Zhiyong Hong
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1993
Things change. We describe these changes mathematically in terms of derivatives. A change of a variable, Φ, with respect to time is simply dΦ/dt. If the variable is also a function of position, the change in the variable depends on the direction. ∂Φ/ ∂x may be different from ∂Φ/ ∂y.
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Things change. We describe these changes mathematically in terms of derivatives. A change of a variable, Φ, with respect to time is simply dΦ/dt. If the variable is also a function of position, the change in the variable depends on the direction. ∂Φ/ ∂x may be different from ∂Φ/ ∂y.
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Differentials and Differential Operations
2017Bernd Steinbach, Christian Posthoff
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Fundamental results to the weighted Caputo-type differential operator
Applied Mathematics Letters, 2021Jian-Gen Liu +2 more
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