Titlebook: Elliptic Partial Differential Equations of Second Order; David Gilbarg,Neil S. Trudinger Book 2001Latest edition Springer-Verlag GmbH Germ

negation

书目名称Elliptic Partial Differential Equations of Second Order影响因子(影响力)




书目名称Elliptic Partial Differential Equations of Second Order影响因子(影响力)学科排名




书目名称Elliptic Partial Differential Equations of Second Order网络公开度




书目名称Elliptic Partial Differential Equations of Second Order网络公开度学科排名




书目名称Elliptic Partial Differential Equations of Second Order被引频次




书目名称Elliptic Partial Differential Equations of Second Order被引频次学科排名




书目名称Elliptic Partial Differential Equations of Second Order年度引用




书目名称Elliptic Partial Differential Equations of Second Order年度引用学科排名




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书目名称Elliptic Partial Differential Equations of Second Order读者反馈学科排名

蚊子

Laplace’s Equationere .. In this chapter we develop some basic properties of harmonic, subharmonic and superharmonic functions which we use to study the solvability of the classical Dirichlet problem for ., . = 0. As mentioned in Chapter 1, Laplace’s equation and its inhomogeneous form, Poisson’s equation, are basic

蜡烛

流浪者

Poisson’s Equation and the Newtonian Potentialion . defined on ℝ. by .. From Green’s representation formula (2.16), we see that when . is sufficiently smooth a ..(.) function may be expressed as the sum of a harmonic function and the Newtonian potential of its Laplacian. It is not surprising therefore that the study of . . = . can largely be ef

Frequency

AWRY

AWRY

Sobolev Spacesquation (2.3)) a C2(Q) solution of .=. satisfies the integral identity . for all . ∈ .. ∈ (.). The bilinear form . is an inner product on the space ..(.) and the completion of ..(.) under the metric induced by (7.2) is consequently a Hubert space, which we call ..(.).

单调性

严厉谴责

Maximum and Comparison Principlesapter 3. We consider second order, quasilinear operators . of the form (10.1) . = ..(., ., .).. + .(., ., .), .. = .., where . = (....., ..) is contained in a domain . of ℝ., . ≥ 2, and, unless other-wise stated, the function . belongs to ..(.). The coefficients of ., namely the functions ..(., ., .

捕鲸鱼叉

Topological Fixed Point Theorems and Their Applicationtes for solutions. This reduction is achieved through the application of topological fixed point theorems in appropriate function spaces. We shall first formulate a general criterion for solvability and illustrate its application in a situation where the required apriori estimates are readily derive