Geometric Properties for Parabolic and Elliptic PDE's

- Poincaré and Hardy Inequalities on Homogeneous Trees. - Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass. - Optimization of the Structural Performance of Non-homogeneous Partially Hinged Rectangular Plates. - Energy-Like Functional in a Quasilinear Parabolic Chemotaxis System. - Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance. - Bounds for Sobolev Embedding Constants in Non-simply Connected Planar Domains. - Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Condition. - Neutral Inclusions, Weakly Neutral Inclusions, and an Over-determined Problem for Confocal Ellipsoids. - Nonexistence of Radial Optimal Functions for the Sobolev Inequality on Cartan-Hadamard Manifolds. - Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games. - An Interpolating Inequality for Solutions of Uniformly Elliptic Equations. - Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method. - A Note on Radial Solutions to the Critical Lane-Emden Equation with a Variable Coefficient. - Remark on One Dimensional Semilinear DampedWave Equation in a CriticalWeighted L 2-space.