Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains

نویسندگان

  • Steve Hofmann
  • John Lewis
  • Marius Mitrea
چکیده

We study the invertibility of λI+K in Lp(∂Ω×R), for p near 2 and λ ∈ R, |λ| ≥ 12 , where K is the caloric double layer potential operator, and Ω is a Lipschitz domain. Applications to transmission boundary value problems are also presented.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Regularity Properties of Commutators and Layer Potentials Associated to the Heat Equation

In recent years there has been renewed interest in the solution of parabolic boundary value problems by the method of layer potentials. In this paper we consider graph domains D = {{x, t): x > /(/)} in SH , where the boundary function / is in /, ,2(BMO). This class of domains would appear to be the minimal smoothness class for the solvability of the Dirichlet problem for the heat equation by th...

متن کامل

Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

متن کامل

Solving Inverse Sturm-Liouville Problems with Transmission Conditions on Two Disjoint Intervals

‎In the present paper‎, ‎some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated‎. ‎Uniqueness theorems for the solution of the inverse problem are proved‎, ‎then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.

متن کامل

Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

متن کامل

Boundary Integral Equations for the Biharmonic Dirichlet Problem on Nonsmooth Domains

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003