Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects

DOI10.1515/acv-2020-0114zbMath1505.35253arXiv2004.03110OpenAlexW3156067136MaRDI QIDQ2677305

Yanyan Li

Publication date: 13 January 2023

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.03110

zbMATH Keywords

monotonicityregularityglobal strong solutionfourth-order degenerate parabolic equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) Initial value problems for higher-order parabolic equations (35K30) PDEs with measure (35R06)

Cites Work

• Unnamed Item
• Unnamed Item
• Scale-invariant extinction time estimates for some singular diffusion equations
• Very singular diffusion equations: second and fourth order problems
• Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
• Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces
• Global strong solution with BV derivatives to singular solid-on-solid model with exponential nonlinearity
• Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces
• Existence Theorems for a Multidimensional Crystal Surface Model
• Derivation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surface
• Existence Theorems for a Crystal Surface Model Involving the $p$-Laplace Operator
• Regularity in Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces
• Gradient flow approach to an exponential thin film equation: global existence and latent singularity
• Analytical Validation of a Continuum Model for the Evolution of a Crystal Surface in Multiple Space Dimensions
• The growth of crystals and the equilibrium structure of their surfaces
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• Continuum theory of epitaxial crystal growth. I.

This page was built for publication: Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects