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Volume 23, Issue 2
Light-like Extremal Surfaces in Minkowski Space R1+(1+n)

Yijie He

DOI: 10.4208/jpde.v23.n2.3

J. Part. Diff. Eq., 23 (2010), pp. 158-167.

Published online: 2010-05

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  • Abstract

In this paper we investigate the equations for light-like extremal surfaces in Minkowski space R^{1+(1+n)}. We show that the light-like assumption is compatible with the Cauchy problem and give a necessary and sufficient condition on the global existence of classical solutions of the Cauchy problem. Based on this, we obtain entire light-like extremal surfaces by solving the Cauchy problem explicitly when such necessary and sufficient condition holds. Finally, some discussions and related remarks are given.

  • Keywords

Light-like extremal surface Cauchy problem global classical solution

  • AMS Subject Headings

35Q75 35G25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-23-158, author = {Yijie He }, title = {Light-like Extremal Surfaces in Minkowski Space R1+(1+n)}, journal = {Journal of Partial Differential Equations}, year = {2010}, volume = {23}, number = {2}, pages = {158--167}, abstract = {

In this paper we investigate the equations for light-like extremal surfaces in Minkowski space R^{1+(1+n)}. We show that the light-like assumption is compatible with the Cauchy problem and give a necessary and sufficient condition on the global existence of classical solutions of the Cauchy problem. Based on this, we obtain entire light-like extremal surfaces by solving the Cauchy problem explicitly when such necessary and sufficient condition holds. Finally, some discussions and related remarks are given.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v23.n2.3}, url = {http://global-sci.org/intro/article_detail/jpde/5226.html} }
TY - JOUR T1 - Light-like Extremal Surfaces in Minkowski Space R1+(1+n) AU - Yijie He JO - Journal of Partial Differential Equations VL - 2 SP - 158 EP - 167 PY - 2010 DA - 2010/05 SN - 23 DO - http://doi.org/10.4208/jpde.v23.n2.3 UR - https://global-sci.org/intro/article_detail/jpde/5226.html KW - Light-like KW - extremal surface KW - Cauchy problem KW - global classical solution AB -

In this paper we investigate the equations for light-like extremal surfaces in Minkowski space R^{1+(1+n)}. We show that the light-like assumption is compatible with the Cauchy problem and give a necessary and sufficient condition on the global existence of classical solutions of the Cauchy problem. Based on this, we obtain entire light-like extremal surfaces by solving the Cauchy problem explicitly when such necessary and sufficient condition holds. Finally, some discussions and related remarks are given.

Yijie He . (2010). Light-like Extremal Surfaces in Minkowski Space R1+(1+n). Journal of Partial Differential Equations. 23 (2). 158-167. doi:10.4208/jpde.v23.n2.3
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