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To do so, a novel definition of discrete maximum principle (DMP) is proposed using the discrete variational setting of the problem, and we show that the fulfilment of this DMP implies that the minimum/maximum (depending on the sign of the forcing term) is on the boundary for multidimensional problems.
Let us present the setting of the problem.
Such a functional setting of the problem in (mathbb{R}^{N}) is key in the following.
In Section 2, we give the basic setting of the problem and derive some priori estimates needed in the proof in next section.
Next we establish the history setting of the problem (1.1 - 1.3 1.1 - 1.3 to deal winh the nordertonomous character of the memory term in (1.1).
In the setting of the problem (1.1), the constraint nondegeneracy condition holding at a feasible point can be expressed as (2.12).
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Let S denote the solution set of the problem (3.8).
In the sequel, we use Γ to denote the solution set of the problem (1.8).
Let (Omeganeqemptyset) be the solution set of the problem MSSEP (3.2).
We will denote by (Omega_{L,T}^{V}) the solution set of the problem (4.5).
We use EP ( F, A ) to denote the solution set of the problem (1.1).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com