Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Integral Representations of Solutions of Periodic Elliptic Equations

The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral representations are analogs of those previously obtained by S. Agmon, S. Helgason, and other authors for solutions of the Helmholtz equation (i.e., for generalized eigenfu...

متن کامل

Gradient bounds for solutions of elliptic and parabolic equations

Let L be a second order elliptic operator on R with a constant diffusion matrix and a dissipative (in a weak sense) drift b ∈ L loc with some p > d. We assume that L possesses a Lyapunov function, but no local boundedness of b is assumed. It is known that then there exists a unique probability measure μ satisfying the equation Lμ = 0 and that the closure of L in L1(μ) generates a Markov semigro...

متن کامل

Integral representations and Liouville theorems for solutions of periodic elliptic equations

The paper contains integral representations for certain classes of exponentially growing solutions of second order periodic elliptic equations. These representations are the analogs of those previously obtained by S. Agmon, S. Helgason, and other authors for solutions of the Helmholtz equation. When one restricts the class of solutions further, requiring their growth to be polynomial, one arriv...

متن کامل

On symmetry of nonnegative solutions of elliptic equations

We consider the Dirichlet problem for a class of fully nonlinear elliptic equations on a bounded domain Ω. We assume that Ω is symmetric about a hyperplane H and convex in the direction perpendicular to H. By a well-known result of Gidas, Ni and Nirenberg and its generalizations, all positive solutions are reflectionally symmetric about H and decreasing away from the hyperplane in the direction...

متن کامل

Elliptic and Parabolic Equations

Elliptic equations: 1. Harmonic functions 2. Perron’s method 3. Potential theory 4. Existence results; the method of suband supersolutions 5. Classical maximum principles for elliptic equations 6. More regularity, Schauder’s theory for general elliptic operators 7. The weak solution approach in one space dimension 8. Eigenfunctions for the Sturm-Liouville problem 9. Generalization to more dimen...

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

ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2007

ISSN: 0022-1236

DOI: 10.1016/j.jfa.2006.12.012