Titlebook: Classical Potential Theory; David H. Armitage,Stephen J. Gardiner Book 2001 Springer-Verlag London 2001 Analysis.Complex Analysis.Harmonic

膠狀

Subharmonic Functions,value property: . (.) = . (.) whenever .. Subharmonic functions correspond to one half of this definition — they are upper-finite, upper semicontinuous functionss which satisfy the mean value inequality . (.) ≤ . (.) whenever .. They are allowed to take the value ?∞ 00 so that we can include such fu

Pander

Polar Sets and Capacity, of Lebesgue measure zero. Indeed, polar sets are the negligible sets of potential theory and will be seen to play a role reminiscent of that played by sets of measure zero in integration. A useful result proved in Section 5.2 is that closed polar sets are removable singularities for lower-bounded s

拋射物

The Dirichlet Problem,) → .(.) as . → . for each .. Such a function . is called the . on Ω with boundary function ., and the maximum principle guarantees the uniqueness of the solution if it exists. For example, if Ω is either a ball or a half-space and . ∈ .(δ.Ω), then the solution of the Dirichlet problem certainly exi

inferno

Boundary Limits,e harmonic function on . has finite non-tangential limits at σ-almost every boundary point (Fatou’s theorem). The notions of radial and non-tangential limits are clearly unsuitable for the study of boundary behaviour in general domains. To overcome this difficulty, we will develop the ideas of the p

琺瑯

Potential Performance Texts for , and ,ved, including the fact that they are “almost” superharmonic. Later, in Section 5.7, deeper properties will be proved via an important result known as the fundamental convergence theorem of potential theory. Before that, however, we will develop the notion of the capacity of a set, beginning with co

Palliation

尊重

Polar Sets and Capacity,ved, including the fact that they are “almost” superharmonic. Later, in Section 5.7, deeper properties will be proved via an important result known as the fundamental convergence theorem of potential theory. Before that, however, we will develop the notion of the capacity of a set, beginning with co

Cabinet

lethal

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