Nature

Cauchy Problems for Helmholtz Equations

The Cauchy problem for the Helmholtz equation has emerged as an important yet challenging subject in applied mathematics and engineering. This problem involves deducing interior solutions from ...
Nature

Cauchy Problems And Inverse Problems In Partial Differential Equations

Cauchy problems and inverse problems in partial differential equations (PDEs) represent a class of challenging mathematical models where one seeks to determine unknown data inside a domain from ...
JSTOR Daily

Minimal Solutions of the Heat Equation and Uniqueness of the Positive Cauchy Problem on Homogeneous Spaces

The minimal positive solutions of the heat equation on X × (-∞, T) are determined for X a homogeneous Riemannian space. A simple proof of uniqueness for the positive Cauchy problem on a homogeneous ...
JSTOR Daily

An Elementary Integral Solution Operator for the Cauchy-Riemann Equations on Pseudoconvex Domains in $C^n$

Transactions of the American Mathematical Society, Vol. 274, No. 2 (Dec., 1982), pp. 809-816 (8 pages) An integral representation formula for $(0, q)$ forms is ...