Bulk-boundary eigenvalues for bilaplacian problems

DOI10.3934/dcds.2022096zbMath1520.35107arXiv2112.05942OpenAlexW4286541929MaRDI QIDQ6160085

María del Mar González, Manuel J. Miranda, Carles Falcó, Davide Buoso

Publication date: 23 June 2023

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.05942

zbMATH Keywords

Cahn-Hilliard equationdomain perturbationdynamic boundary conditionseigenvalue bifurcationbilaplacian eigenvaluesbulk-boundary eigenvalueseigenfunctions on balls and annulus

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Classical solutions to PDEs (35A09)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multi-layer potentials and boundary problems for higher-order elliptic systems in Lipschitz domains
• The Steklov spectrum on moving domains
• On a class of non-local operators in conformal geometry
• An isoperimetric inequality for fundamental tones of free plates
• The first Steklov eigenvalue, conformal geometry, and minimal surfaces
• A Cahn-Hilliard model in a domain with non-permeable walls
• The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization
• On asymptotic properties of biharmonic Steklov eigenvalues
• On positivity for the biharmonic operator under Steklov boundary conditions
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• On the first eigenvalue of a fourth order Steklov problem
• On the fundamental eigenfunctions of a clamped punctured disk
• The zeta functional determinants on manifolds with boundary. I: The formula
• The zeta functional determinants on manifolds with boundary. II: Extremal metrics and compactness of isospectral set
• On the stability of some isoperimetric inequalities for the fundamental tones of free plates
• Eigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problems
• An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis
• On the explicit representation of the trace space \(H^{\frac{3}{2}}\) and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems
• On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: well-posedness, regularity theory and eigenvalue problems
• From Steklov to Neumann via homogenisation
• A few shape optimization results for a biharmonic Steklov problem
• Spectral asymptotics for the Laplacian under an eigenvalue dependent boundary condition
• Inequalities for membrane and Stekloff eigenvalues
• On the nonlocal Cahn-Hilliard equation with nonlocal dynamic boundary condition and boundary penalization
• Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator
• Vibrational modes of circular free plates under tension
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• On a fourth order Steklov eigenvalue problem
• The Neumann problem on Lipschitz domains
• Weakly Differentiable Functions
• $L^2$-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
• Boundary operators associated with the Paneitz operator
• Phase-field dynamics with transfer of materials: The Cahn–Hilliard equation with reaction rate dependent dynamic boundary conditions
• The Bilaplacian with Robin Boundary Conditions
• Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach
• An Extension Problem Related to the Fractional Laplacian
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• The buckling eigenvalue problem in the annulus