We study well-posedness and asymptotic behaviour of the
equation with dynamic boundary condition. This modification of the
non-flux condition has been introduced to incorporate surface
means of optimal regularity results in the L_p-setting for the
linearized problem, well-posedness and the global semiflow in an
appropriate phase space are obtained. We also show convergence of
solutions to equilibrium states in energy norm. This result is
via the recent Lojasiewicz technique.
I shall present a result of Zabreiko regarding the
continuity of a countably subadditive seminorm on a Banach space
and show how several major theorems in functional analysis like
Uniform Boundedness Principle, Closed Graph Theorem, Open Mapping
Theorem etc. can be easily derived from this result.
We discuss some recent work on a family of weighted
Hardy-Sobolev inequalities due to Caffarelli-Kohn-Nirenberg
including symmetry property and symmetry breaking of extremal
improved Hardy inequalities, as well as bound state solutions to
the associated nonlinear PDEs.
We will talk about curvature flows and their regularity theory.
The theorem is a DeGorgi type regularity but the monotonicity formula is lacking in our cases.
This is a learning seminar on the Inverse Scatering theory.
This talk is concerned with several eigenvalue problems from a linear stability analysis for the steady state morphogen gradients in Drosophila wing imaginal discs. These problems share several common difficulties including the followings: 1) The steady state solution which occurs in the coefficients of the relevant differential equations of the stability analysis is only know qualitatively and numerically. 2) Though the governing differential equations are linear, the eigenvalue parameter appears nonlinearly in the differential equations as well as in the boundary conditions.
The goal of the talk is to discuss some recent results
joint work with Bernhard Lamel) concerning the structure of the
global groups of CR automorphisms of real-analytic CR manifolds,
levi-form is allowed to degenerate. We will mainly focus on the
real-analytic hypersurfaces containing no holomorphic curves and
show that in
such a setting the local automorphism groups can be analytically
by a finite jet at any given point.
We discuss some old and new results on ideals,
characters, and finite matrices of the algebra of holomorphic functions on a pseudoconvex open set in Banach spaces with countable unconditional bases.