Positivity for a strongly coupled elliptic system by Green function estimates

DOI10.1007/BF02921596zbMath0792.35048MaRDI QIDQ1323557

Guido Sweers

Publication date: 30 June 1994

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

maximum principleGreen functionelliptic systems on bounded domainspointwise bounds for the lifetimeSchechter type spaces

Mathematics Subject Classification ID

Related Items (22)

Nonlinear equations and weighted norm inequalities ⋮ Unnamed Item ⋮ On the Lifetime of a Conditioned Brownian Motion in Domains Connected Through Small Gaps ⋮ Comparison principle for non-cooperative elliptic systems ⋮ On the lifetime of a conditioned Brownian motion in the ball ⋮ Weakly Coupled Elliptic Systems and Positivity ⋮ Existence and uniqueness of positive solution for non-variational elliptic systems ⋮ Positivity for the Navier bilaplace, an anti-eigenvalue and an expected lifetime ⋮ A comparison result for perturbed radial \(p\)-Laplacians. ⋮ On positivity for the biharmonic operator under Steklov boundary conditions ⋮ Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions ⋮ Estimates of invariant distances on ``convex domains ⋮ Criterion for the Sobolev well-posedness of the Dirichlet problem for the Poisson equation in Lipschitz domains. I ⋮ Local and global maxima for the expectation of the lifetime of a Brownian motion on the disk ⋮ Uniform bounds for higher-order semilinear problems in conformal dimension ⋮ Nonvariational problems with critical growth ⋮ Among all two-dimensional convex domains the disk is not optimal for the lifetime of a conditioned Brownian motion ⋮ Separating positivity and regularity for fourth order Dirichlet problems in 2d-domains ⋮ Positivity results for a nonlocal elliptic equation ⋮ On a conditioned Brownian motion and a maximum principle on the disk ⋮ Some symmetric boundary value problems and non-symmetric solutions ⋮ Matrix Dirichlet problem with applications to hinged beam differential equations

Cites Work

• Strong positivity in \(C(\bar\Omega)\) for elliptic systems
• Green function for Schrödinger operator and conditioned Feynman-Kac gauge
• Conditional transformation of drift formula and potential theory for \(\Delta +b(\cdot)\cdot \nabla\)
• Uniform bounds for quotients of Green functions on \(C^{1,1}\)-domains
• Schrödinger semigroups
• Conditional brownian motion and the boundary limits of harmonic functions
• Lifetime of conditioned Brownian motion in Lipschitz domains
• Conditional Gauge and Potential Theory for the Schrodinger Operator
• Further results on maximum principles for noncooperative elliptic systems
• Elliptic Partial Differential Equations of Second Order
• A Strong Maximum Principle for a Noncooperative Elliptic System
• The lifetime of conditioned Brownian motion
• Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations.
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