On the iterative and minimizing sequences for semilinear elliptic equations (I)
Copyright policy )On the iterative and minimizing sequences for semilinear elliptic equations (I)
Les auteurs continuent leur précédente recherche [ibid. 12, No. 2, 309-326 (1995; Zbl 0842.35004)] sur la solution numérique de l'équation elliptique semilinéaire (1) \(-\Delta u= f(u)\) dans \(\Omega\), avec la condition (2) \(u=0\) sur \(\partial \Omega\), où \(\Omega\) est un domaine polygonal à deux dimension. Nous remarquons le théorème (1.1) sur la construction d'une succession, qui a une sous-succession convergente en \(H^1(\Omega) \cap L^\infty (\Omega)\) à une solution instable du problème (1)--(2), où \(H^1 (\Omega)= W^{1,2} (\Omega)\) est l'espace de Sobolev.
- Osaka University Japan
- Gakushuin University Japan
- Ehime University Japan
Variational methods for second-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, Lagrange multiplier, polygonal domain, Theoretical approximation in context of PDEs, uniform convergence of minimizing sequence, instable solution
Variational methods for second-order elliptic equations, Nonlinear boundary value problems for linear elliptic equations, Lagrange multiplier, polygonal domain, Theoretical approximation in context of PDEs, uniform convergence of minimizing sequence, instable solution
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