OBSTACLE PROBLEMS FOR SCALAR GINZBURG-LANDAU EQUATIONS
摘要
In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation △u =f(x, u). This will give an estimate of the Hausdorff dimension for the free boundary of the obstacle problem.
参考文献6
-
1Friedman A, Free boundary problems in science and technology, Notices AIDS,47(8)(2000), 854-861.
-
2Caffarelli L A , The obstacle problem revisited, J Fourier Anal. Appl., 4(1998), 383-402.
-
3Lee K and Shahgholian H, Hausdorff dimension and stability for the p-obstacle problem (2 < p), Preprint, 2001.
-
4Choe H J and Lewis J L , On the obstacle problem for quasilnear elliptic equations of p-laplacian type, SIAM, J Math. Anal, 22(3)(1991), 623-638.
-
5Caffarelli L A , Karp L , H Shahgholian, Regularity of a free boundary with application to the Pompeiu problem, Ann. Math., 151(2000), 269-292.
-
6Gilbarg D and Trudinger N S , Elliptic Partial Differential Equations of Second Order,Springer-Verlag, Berlin/New York, 1983.
-
1杨健夫.REGULARITY OF WEAK SOLUTIONS TOQUASILINEAR ELLIPTIC OBSTACLE PROBLEMS[J].Acta Mathematica Scientia,1997,17(2):159-166. 被引量：2
-
2苏剑,王立周.Regularity of solutions of obstacle problems[J].Journal of Pharmaceutical Analysis,2007,19(1):7-8.
-
3LIU ZUHAN Department of Mathematics, Normal College. Yangzhou University. Yangzhou 225002, China. E-mail: zuhanl@yahoo.com.DYNAMICS FOR VORTICES OF AN EVOLUTIONARY GINZBURG-LANDAU EQUATIONS IN 3 DIMENSIONS[J].Chinese Annals of Mathematics,Series B,2002,23(1):95-108. 被引量：5
-
4郭伯灵,王碧祥.WEAK SOLUTIONS TO THE TWO-DIMENSIONAL DERIVATIVE GINZBURG-LANDAU EQUATION[J].Acta Mathematicae Applicatae Sinica,1999,15(1):1-8.
-
5黄海洋.EXISTENCE OF PERIODIC SOLUTIONS OF THE BURGERS-GINZBURG-LANDAU EQUATIONS[J].Acta Mathematica Scientia,2004,24(4):613-622.
-
6ZHAO Chunshan.Remark on Exponential Decay of Ground States for N-Laplacian Equations[J].Journal of Partial Differential Equations,2009,22(1):32-41.
-
7Bo-ling Guo, Hai-yang HuangCenter of Nonlinear Studies, Institute of Applied Physics and Computational Mathematics. P.O. Box 8009. Beijing 100088, ChinaDepartment of Mathematics. Beijing Normal University, Beijing 100875, China.Well-posedness and Global Attractors for the Burgers-Ginzburg-Landau Equations[J].Acta Mathematicae Applicatae Sinica,2002,18(4):579-588.
-
8Xiao Qishan (Dept. of Math. and Computer Science, Fujian Radio TV University, Fuzhou 350003).A STRONG MAXIMUM PRINCIPLE FOR p(x)-LAPLACIAN EQUATION[J].Annals of Differential Equations,2008,24(3):356-360.
-
9陈淑红,郭柏灵.CLASSICAL SOLUTIONS OF GENERAL GINZBURG-LANDAU EQUATIONS[J].Acta Mathematica Scientia,2016,36(3):717-732.
-
10CHEN Shuhong GUO Boling.On the Cauchy Problem of the Ginzburg-Landau Equations for Atomic Fermi Gases Near the BCS-BEC Crossover[J].Journal of Partial Differential Equations,2009,22(3):218-233. 被引量：4
