A Parabolic Approach to Martin Boundaries for Elliptic Equations in Skew Product Form

作者：Murata Minoru; Suzuki Noriaki^*

来源：Potential Analysis, 2014, 40(3): 279-305.

DOI：10.1007/s11118-013-9353-x

• Martin boundary
• Elliptic equation
• Skew product
• Nonnegative solution
• Integral representation
• Semismall perturbation
• Intrinsic ultracontractivity
• Parabolic equation
• Uniqueness for the positive Cauchy problem

We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin compactifications and Martin kernels for a wide class of elliptic equations in skew product form by exploiting parabolic Martin kernels for associated parabolic equations.

• 出版日期2014-4