Elliptic Problems in Nonsmooth Domains |
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Page vii
... singular solutions 261 5.2 Operators with variable coefficients 265 6 Results in spaces of Hölder functions 274 6.1 ... Singular solutions , the L2 case 305 7.2.1 Kondratiev's method in weighted spaces 305 7.2.2 Getting rid of the ...
... singular solutions 261 5.2 Operators with variable coefficients 265 6 Results in spaces of Hölder functions 274 6.1 ... Singular solutions , the L2 case 305 7.2.1 Kondratiev's method in weighted spaces 305 7.2.2 Getting rid of the ...
Page 305
... Singular solutions , the ↳2 case 7.2.1 Kondratiev's method in weighted spaces ( 7,1,2 ) In this section we shall study the problem ( 7,1,2 ) in the framework of the ... Singular solutions, the L2 case Kondratiev's method in weighted spaces.
... Singular solutions , the ↳2 case 7.2.1 Kondratiev's method in weighted spaces ( 7,1,2 ) In this section we shall study the problem ( 7,1,2 ) in the framework of the ... Singular solutions, the L2 case Kondratiev's method in weighted spaces.
Page 384
... solution near the corners ( see details in Subsection 8.4.1 ) . The second consists in augmenting the space of trial functions in which one looks for the approximate solution . This is done by adding some of the singular solutions of ...
... solution near the corners ( see details in Subsection 8.4.1 ) . The second consists in augmenting the space of trial functions in which one looks for the approximate solution . This is done by adding some of the singular solutions of ...
Contents
Regular secondorder elliptic boundary value problems | 81 |
Secondorder elliptic boundary value problems in convex | 132 |
Secondorder elliptic boundary value problems in polygons | 182 |
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a₁ Accordingly apply Theorem B₁ belongs boundary conditions boundary value problems bounded open subset C₁ C¹¹ C² boundary Chapter coefficients Consequently convex coordinates corners Corollary corresponding cosh curvilinear polygon cut-off function defined Definition denote derivatives Dirichlet problem domains dx dy equation exists a constant exists a unique finite follows fulfils the boundary g₁ Green formula H¹(N H²(N Hölder Hölder continuous Hölder spaces holds identity implies inequality integer k₁ Lipschitz boundary Lipschitz continuous mapping neighbourhood Neumann problem norm notation obviously partition of unity plane Proof of Lemma proof of Theorem properties prove real numbers Remark result S₁ Section sequence shows singular solutions sinh smooth Sobolev spaces solution of problem subspace Ti.h u₁ V₁ vanishes vector Xn+1 zero πθ ди дт მა