Singularly perturbed elliptic boundary value problems. I: Poisson kernels and potential theory

DOI10.1007/BF02415045zbMath0229.35030OpenAlexW197027357MaRDI QIDQ2550129

Paul C. Fife

Publication date: 1971

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02415045

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Asymptotic expansions of solutions to PDEs (35C20)

Related Items (7)

Coercive singular perturbations II: reduction to regular perturbations and applications ⋮ Coercive singular perturbations. I: A priori estimates ⋮ The resolvent of a singularly perturbed elliptic operator ⋮ General boundary value problems for ordinary differential equations with small parameter ⋮ Perturbazioni singolari ellittiche ⋮ Perturbazioni singolari per un problema quasi-ellittico a coefficienti costanti nel semispazio ⋮ Coercive singular perturbations. II: Reduction and convergence

Cites Work

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• Elliptic boundary problems with a small parameter
• Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type
• Singular perturbations for partial differential equations
• Rate of convergence in singular perturbations
• The first boundary value problem for \(\epsilon\Delta u+A(x,y)u_x+B(x,y)u_y+C(x,y)u =D(x,y)\) for small \(\epsilon\)
• Asymptotic solution of boundary value problems for the differential equation \(\Delta U+\lambda\partial U/\partial x=\lambda f(x,y)\)
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Non-linear deflection of thin elastic plates under tension

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