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With the decreasing properties of gradient modulus of subdivision finite element, it has been proved that the function sequence converges to the solution of finite element formulation of p-Laplace equation.
According to theoretical analysis in Sections 4 and 5, the particular initial function can lead to a particular sequence of iterative function with the decreasing properties of gradient modulus on each element e, it is further proved to converge to the solution for p-Laplace equation.
By the Newton iteration with step length 1, the particular initial function results in a particular sequence of iterative functions with the decreasing properties of the gradient modulus of a subdivision element, and it is proved to converge to the solution of finite element formulation of the p-Laplace equation in Section 4.
We can find similar kind of decreasing properties but less explicit than in the linear case.
On the other hand, since the decreasing properties and existence of nontrivial lower boundary, these iterative functions are all well posed, whereas the well-posed theorem in Section 3.2 cannot guarantee that the subsequent functions of iteration are always well posed.
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Further, it is easily seen that inherits the monotone decreasing property of.
Now let's prove the monotonically decreasing property of Y γ 0 in terms of γ0. 1.
It is not hard to see that ((mathbb{R}^,tau(d_{S}),leq)) has the orbital decreasing property with respect to f.
Example 10 shows that the orbital decreasing property cannot be omitted in the statement of Corollary 15 in order to guarantee the uniqueness of the fixed point.
The trend of higher proportions of the NS-SEC never worked and long-term unemployed category of respondents and more deprived mean Townsend scores with decreasing property value is clear.
Some people worried about decreased property values and increased crime, and Community Board 2's social services committee initially rejected the idea.
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