The results of A. P. Calderón concerning unique continuation of solutions of elliptic equations with "simple characteristics" are proved, with some extensions, using the method of the first part of ...

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 ...

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 ...

SIAM Journal on Applied Mathematics, Vol. 34, No. 1 (Jan., 1978), pp. 37-54 (18 pages) The equivalence of the methods for solving both the Goursat problem and the Cauchy problem for the sine-Gordon ...