Partial differential equations and spatial structures of Lévy Type : uncertainty quantification and optimization / von Marco Reese. Wuppertal, [2021]
Content
- Introduction
- Linear Partial Differential Equations
- Hölder Spaces
- Regularity Properties of Domains
- Sobolev Spaces
- Elliptic System of Linear Partial Differential Equation
- Generalized Random Fields
- Multi-Hilbertian Spaces
- Generalized Random Fields
- Lévy Random Fields
- Smoothed Stationary Noise Fields
- Examples
- An Analytical Study in Multi-Physics and Multi-Criteria Shape Optimization
- Probabilistic Life Prediction
- A Multi-Criteria Shape Optimization Problem
- Multi-Physics Shape Optimization
- Multi-Physics Equation Coupling
- Admissible Shapes and Criteria
- Examples
- Multi-Physics Shape Optimization Problem
- Existence of Pareto Optimal Shapes
- Scalarization and Multi-Physics Optimization
- Integrability and Approximability of Solutions to the Stationary Diffusion Equation with Lévy Coefficient
- Conclusion