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AFEM for the Laplace-Beltrami Operator on Graphs: Design and Conditional Contraction Property
Laplace-Beltrami operator graphs adaptive fi nite element method
2015/12/11
We present an adaptive finite element method (AFEM) of any polynomial degree for the
Laplace-Beltrami operator on C
1
graphs Γ in R
d
(d ≥ 2). We first derive residual-type a
posteri...
Optimal relations between Lp-norms for the Hardy operator and its dual
Hardy operator Dual operator Best constants
2012/6/29
We obtain sharp two-sided inequalities between $L^p-$norms $(1ere $H$ is the Hardy operator, $H^*$ is its dual, and $f$ is a nonnegative measurable function...
Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1
Notes area operator geometric 2-rough paths Young integral
2012/4/17
1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral i...
On Generalized Solution of a Class of Higher Order Operator-Differential Equations
Operator-differential equations Hilbert spaces existence of generalized solution
2010/2/25
In this paper the sufficient conditions on the existence and uniqueness of a generalized solution on the axis are obtained for higher order operator-differential equations, the main part of which is m...