On uniqueness, stability and pointwise estimates in the Cauchy problem for coupled elliptic equations

Author:
Philip W. Schaefer

Journal:
Quart. Appl. Math. **31** (1973), 321-328

MSC:
Primary 35J45

DOI:
https://doi.org/10.1090/qam/430523

MathSciNet review:
430523

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Abstract: Results of the kind cited in the title are obtained for the improperly posed Cauchy problem for a system of two coupled elliptic partial differential equations. We assume one stabilizing condition is imposed on one of the dependent variables. The results follow from an a priori inequality which is derived as a consequence of the logarithmic convexity of a suitable functional.

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Additional Information

DOI:
https://doi.org/10.1090/qam/430523

Article copyright:
© Copyright 1973
American Mathematical Society