Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function

DOI10.1017/S0308210500020102zbMath0481.35022MaRDI QIDQ3937729

Lawrence E. Payne

Publication date: 1981

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

comparison theoremstorsion problemclamped membrane problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Plates (74K20) Maximum principles in context of PDEs (35B50) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (14)

SHARP UPPER AND LOWER SOLUTIONS IN SOME PARABOLIC PROBLEMS ⋮ Brownian motion and the fundamental frequency of a drum ⋮ Comparison results in second order quasilinear Dirichlet problems ⋮ Pointwise Lower Bounds for Solutions of Semilinear Elliptic Equations and Applications ⋮ Spectral bounds for the torsion function ⋮ Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian ⋮ On two functionals involving the maximum of the torsion function ⋮ Optimal bounds in semilinear elliptic problems with nonlinear boundary conditions ⋮ On a Pólya functional for rhombi, isosceles triangles, and thinning convex sets ⋮ Comparison theorems for a class of nonlinear elliptic boundary value problems ⋮ On the \({ L}^{ p}\) norm of the torsion function ⋮ Optimal sub- or supersolutions in reaction-diffusion problems ⋮ Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle ⋮ Spectral upper bound for the torsion function of symmetric stable processes

Cites Work

• Unnamed Item
• On the torsion function, Green's function and conformal radius: An isoperimetric inequality of Polya and Szegö, some extensions and applications
• Existence theorems, qualitative results and priori bounds for a class of non-linear Dirichlet problems
• On maximum principles for a class of nonlinear second-order elliptic equations
• On the mean value of the fundamental mode in the fixed membrane problem
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature

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