scholarly journals A characterization of first order nonlinear partial differential operators on Sobolev spaces

1980 ◽  
Vol 38 (1) ◽  
pp. 118-138 ◽  
Author(s):  
M Marcus ◽  
V.J Mizel
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Partial Differential ◽  
First Order ◽  
Partial Differential Operators

scholarly journals On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

2014 ◽  
Vol 22 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Jan Chvalina ◽  
Šárka Hošková-Mayerová
Keyword(s):  
Differential Operators ◽  
Partial Differential ◽  
First Order ◽  
Ordered Groups ◽  
Partial Differential Operators ◽  
Power Set

AbstractThe contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

Characterization of Eigenfunctions by Boundedness Conditions

1992 ◽  
Vol 35 (2) ◽  
pp. 204-213 ◽  
Author(s):  
Ralph Howard ◽  
Margaret Reese
Keyword(s):  
Growth Condition ◽  
Constant Coefficient ◽  
Polynomial Growth ◽  
Differential Operators ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Linear Partial Differential Operators ◽  
Sequence Of Functions

AbstractSuppose is a sequence of functions on ℝn with Δfk = fk+1 (where Δ is the Laplacian) that satisfies the growth condition: |fk(x)| ≤ Mk{1 + |x|)a where a ≥ 0 and the constants have sublinear growth Then Δf0 = —f0- This characterizes eigenfunctions f of Δ with polynomial growth in terms of the size of the powers Δkf, —∞ < k < ∞. It also generalizes results of Roe (where a = 0, Mk = M, and n = 1 ) and Strichartz (where a = 0, Mk = M for n). The analogue holds for formally self-adjoint constant coefficient linear partial differential operators on ℝn.

scholarly journals Two-scale convergence with respect to measures and homogenization of monotone operators

2005 ◽  
Vol 3 (2) ◽  
pp. 125-161 ◽  
Author(s):  
Dag Lukkassen ◽  
Peter Wall
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Monotone Operators ◽  
Partial Differential ◽  
Homogenization Problem ◽  
Partial Differential Operators ◽  
Basic Facts

In 1989 Nguetseng introduced two-scale convergence, which now is a frequently used tool in homogenization of partial differential operators. In this paper we discuss the notion of two-scale convergence with respect to measures. We make an exposition of the basic facts of this theory and develope it in various ways. In particular, we consider both variableLpspaces and variable Sobolev spaces. Moreover, we apply the results to a homogenization problem connected to a class of monotone operators.

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