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EXAMPLES OF SEPARATION OF VARIABLES AND APPLICATIONS
LAPLACE EQUATION IN TWODIMENSIONAL PROBLEMS
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additive constant algebraic analogue associated vector asymptotic boundary layers characteristic exponent classical compact resolvent complex value components computation convergence corresponding course crack defined denotes depend derived dihedron dimensional elasticity Dirichlet boundary conditions easily seen edge eigenvalue eigenvectors elasticity problem elasticity system elliptic equation existence Figure finite element method framework given gives Grad gradient Grisvard holomorphic function ij 3x ijkh infinity instance integrable interface isotropic Jordan block Laplace operator leading order Lect Lecture LEMMA linear logarithmic matrix mesh moduli Moreover neighbourhood Neumann boundary conditions Neumann problem normal numerical obtain outer expansion perturbation piecewise plate polar coordinates Proposition 2.1 refracted flux regularity theory REMARK resp respect right hand side satisfying Sect singular exponent singular point singular solution smooth space variables strain stress intensity factor stress tensor subdomain symmetric Theorem three dimensional traction vanish variational formulation vicinity zero