Classical solutions up to the boundary to some higher order semilinear Dirichlet problems

DOI10.1016/j.na.2021.112265zbMath1466.35122OpenAlexW3125342090MaRDI QIDQ2019301

Inka Schnieders, Guido Sweers

Publication date: 20 April 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2021.112265

zbMATH Keywords

regularityDirichlet boundary conditionsclassical solutiongrowth conditionhigher order semilinear elliptic problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Higher-order elliptic equations (35J30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

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Optimal estimates from below for Green functions of higher order elliptic operators with variable leading coefficients

Cites Work

• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Optimal estimates from below for biharmonic Green functions
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Existence and regularity of weak solutions to the Dirichletproblem for semilinear elliptic systems of higher order.
• Classical solutions for some higher order semilinear elliptic equations under weak growth conditions
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