2-Dimensional Lp-Minkowski problem
Topic
et S^{n-1}subset R^n be the unit sphere. The L_p-Minkowski problem
proposed by Lukwak is a natural generalization of the classical
Minkowski problem. Analytically, it is equivalent to find positive
solutions of the equation
det(
abla_{ij}u+e_{ij}u)=g(x)u^{p-1}, xin S^{n-1}, (1)
where g is a function on S^{n-1}, pin f R, e_{ij} is the standard Riemannian metric. In this talk we will present some existence results for the case n=2, that is, 2pi and positive solutions of the equation
''u+u=g(x)u^{p-1}, xin S1 (2)
based on variational method. Some generalizations of equation (2) will also be discussed.
det(
abla_{ij}u+e_{ij}u)=g(x)u^{p-1}, xin S^{n-1}, (1)
where g is a function on S^{n-1}, pin f R, e_{ij} is the standard Riemannian metric. In this talk we will present some existence results for the case n=2, that is, 2pi and positive solutions of the equation
''u+u=g(x)u^{p-1}, xin S1 (2)
based on variational method. Some generalizations of equation (2) will also be discussed.
Speakers
Additional Information
DG-MP-PDE Seminar 2007
Meiyue Jiang (Peking University)
Meiyue Jiang (Peking University)