A sharp trace Adams inequality in ℝ4 and existence of the extremals
Abstract
Let ⊆ ޒ 4 be a bounded domain with smooth boundary ∂ .In this paper, we establish the following sharp form of the trace Adams inequality in W 2,2 ( ) with zero mean value and zero Neumann boundary condition:holds if and only if α ≤ 12π 2 .Moreover, we prove a classification theorem for the solutions of a class of nonlinear boundary value problem of biharmonic equations on the half-space ޒ 4 + .With this classification result, we can show that S(12π 2 ) is attained by using the blow-up analysis and capacitary estimate.As an application, we prove a sharp trace Adams-Onofri-type inequality in general four-dimensional bounded domains with smooth boundary.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Numerical methods in inverse problems
Publication details
- Journal / source
- Analysis & PDE
- Volume
- 19
- Issue
- 3
- Pages
- 413–448
- Publication date
- 11 March 2026
- Language
- EN