Titlebook: Boundary Value Problems and Markov Processes; Functional Analysis Kazuaki Taira Book 2020Latest edition Springer Nature Switzerland AG 202

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Analytic SemigroupsThis chapter is devoted to a review of standard topics from the theory of analytic semigroups which forms a functional analytic background for the proof of Theorems 1.4 and 1.5.

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Theory of Elliptic Boundary Value ProblemsIn this chapter we consider the non-homogeneous general Robin problem . under the following two conditions (H.1) and (H.2) (corresponding to conditions (A) and (B) with . = . and . = −.):.(H.1) .(..) ≥ 0 and .(..) ≥ 0 on ...(H.2) .(..) + .(..) > 0 on ...Here . = −. is the unit . normal to the boundary . (see Figure 6.1 below).

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Proofs of Theorems 1.8, 1.9, 1.10 and 1.11In this chapter we prove Theorems 1.8, 1.9, 1.10 and 1.11, generalizing Theorems 1.4, 1.5 and 1.6 for second-order, elliptic Waldenfels operators.

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