Obtuse cones in Hilbert spaces and applications to partial differential equations

DOI10.1016/0022-1236(80)90088-9zbMath0443.46008OpenAlexW2007287749MaRDI QIDQ1144235

Carole L. Grover, Charles V. Coffman

Publication date: 1980

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(80)90088-9

zbMATH Keywords

Dirichlet problemelliptic operatorsobtuse conegeneralized Sobolev spacedual conecoercive non- symmetric bilinear formspartially ordered Hilbert spacestrongly continuous semi-groups of contractive linear operatorssuperbiharmonic functions with zero Dirichlet boundary values

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Groups and semigroups of linear operators (47D03) Ordered topological linear spaces, vector lattices (46A40) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (14)

Polyhedricity of convex sets in sobolev space ⋮ Differential equations in a Banach space ⋮ Nonlinear potentials in function spaces ⋮ Regions of positivity for polyharmonic Green functions in arbitrary domains ⋮ On sign preservation for clotheslines, curtain rods, elastic membranes and thin plates ⋮ Effect of decay rates of initial data on the sign of solutions to Cauchy problems of polyharmonic heat equations ⋮ Nonlinear questions in clamped plate models ⋮ Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations ⋮ On the structure of biharmonic functions satisfying the clamped plate conditions on a right angle ⋮ On Green's function and eigenvalues of nonuniformly elliptic boundary value problems ⋮ On the fundamental eigenfunctions of a clamped punctured disk ⋮ Epidifferentiability of the map of infima in Hilbert spaces ⋮ Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions ⋮ A biharmonic equation with singular nonlinearity

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