Boundary Behavior of Solutions to Elliptic Equations in General Domains

  • Vladimir G. Maz'ya

    Linköping University, Sweden and University of Liverpool, UK
Boundary Behavior of Solutions to Elliptic Equations in General Domains cover
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FrontmatterDownload pp. i–v
ContentsDownload pp. vii–xi
IntroductionDownload pp. 1–5
1Behavior near the boundary of solutions to the Dirichlet problem for a second-order elliptic equationpp. 7–66
2An analogue of theWiener criterion for the Zaremba problem for the Laplacian in a half-cylinderpp. 67–85
3Wiener type test for the Zaremba problem for degenerate elliptic operators in a half-cylinderpp. 87–112
4Modulus of continuity of solutions to quasilinear elliptic equationspp. 113–131
5Discontinuous solution to the pp-Laplace equationpp. 133–151
6Wiener test for higher-order elliptic equationspp. 153–190
7Wiener test for the polyharmonic equationpp. 191–203
8Weighted positivity andWiener regularity of a boundary point for the fractional Laplacianpp. 205–226
9Wiener type regularity of a boundary point for the 3D Lamé systempp. 227–245
10Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equationpp. 257–295
11Boundedness of derivatives of solutions to the Dirichlet problem for the polyharmonic equationpp. 297–356
12Polyharmonic capacities and higher-order Wiener testpp. 357–418
Bibliographypp. 419–428
General Indexpp. 429–430
Index of Mathematiciansp. 431