NEW APPROXIMATION OF CAUCHY PROBLEM FOR ELLIPTIC EQUATIONS WITH INTEGRAL CONDITION
DOI:
https://doi.org/10.5281/5bk2ft84Abstract
In this paper, we deal with a Cauchy problem for homogeneous
elliptic equation with nonlocal integral condition. We examine and study both
the well-posedness and the non-wellposedness of the mild solutions. In part 2,
we show that the problem is ill-posed in the sense of Hadamard. We propose
a nonlocal regularized problem for approximating the problem. Under some
priori assumptions on the exact solution, we establish some stability estimates
of H¨older type.
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