B. Estimating the local Lipschitz Constant of the entropy operator Bν,q

B.1 Introduction

Local Lipschitz constant estimation represents an analytic-numerical procedure. Therefore, prior to passing to formulation and solution of these problems, it seems reasonable to discuss the basic stages of the above procedure.

We begin with mathematical definitions of the operator Bν,q and its normal form e9783110339024_i3253.jpg. Also we establish relations between them and their key properties such as existence and uniqueness.

All subsequent research involves the normal form of this operator and bases on the following “classic” inequality (see [5]):

(B.1)

where ui ≥ 0, αi ≥ 0, ...

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