Skip to main content Accessibility help
×
Home

Uniqueness Theorems for a Singular Partial Differential Equation

  • P. Ramankutty (a1)

Extract

A singular partial differential equation which occurs frequently in mathematical physics is given by

where is the Laplacian operator on R n of which the generic point is denoted by x = (x1, … , xn) and s and k are real numbers. The study of solutions of this equation for the case k = 0 was initiated by A. Weinstein [5], who named it ‘Generalized Axially Symmetric Potential Theory'. Numerous references to the literature on this equation can be found in [1; 3; 6]. The analytic theory of equations of the type mentioned above has extensively been treated in [2].

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Uniqueness Theorems for a Singular Partial Differential Equation
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Uniqueness Theorems for a Singular Partial Differential Equation
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Uniqueness Theorems for a Singular Partial Differential Equation
      Available formats
      ×

Copyright

References

Hide All
1. Colton, D. and Gilbert, R. P., A contribution to the Vekua-Rellich theory of metaharmonic functions, Amer. J. Math. 92 (1970), 525540.
2. Gilbert, R. P., Function theoretic methods in the theory of partial differential equations (Academic Press, New York, 1969).
3. Gilbert, R. P., An investigation of the analytic properties of solutions to the generalized axially symmetric, reduced wave equation in n + 1 variables, with an application to the theory of potential scattering, SIAM J. Appl. Math. 16 (1968), 3050.
4. Hopf, E., ElementareBemerkungenüber die LosungenpartiellerDifferentialgleichungen ZweiterOrdnungvomelliptichenTypus, S.-B.Preuss.Akad.Wiss. 19 (1927), 147152.
5. Weinstein, A., Generalized axially symmetric potential theory, Bull. Amer. Math. Soc. 59 (1953), 2038.
6. Weinstein, A., Singular partial differential equations and their applications, Proceedings of the symposium on fluid dynamics and applied mathematics, University of Maryland, 1961 (Gordon and Breach, New York, 2949).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Uniqueness Theorems for a Singular Partial Differential Equation

  • P. Ramankutty (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed