Partial regularity for weak solutions of nonlinear elliptic systems: the subquadratic case
作者： Lisa Beck
DOI: 10.1007/S00229-007-0100-8
关键词:
摘要: We consider weak solutions of second order nonlinear elliptic systems divergence type under subquadratic growth conditions. Via the method $${\mathcal{A}}$$ -harmonic approximation we give a characterization regular points up to boundary which extends known results from quadratic and superquadratic case. The proof yields directly optimal higher regularity on set.
springer.com
unirioja.es
core.ac.uk
sci-hub.se 参考文章(23)
A. A. Arkhipova, Partial Regularity up to the Boundary for Weak Solutions of Elliptic Systems with Nonlinearity q Greater Than Two Journal of Mathematical Sciences. ,vol. 115, pp. 2735- 2746 ,(2003) , 10.1023/A:1023361517495
Christoph Hamburger, Partial boundary regularity of solutions of nonlinear superelliptic systems Bollettino Della Unione Matematica Italiana. ,vol. 10, pp. 63- 82 ,(2007)
Enrico Giusti, Direct methods in the calculus of variations World Scientific. ,(2003) , 10.1142/5002
B. Dacorogna, Direct Methods in the Calculus of Variations ,(1989)
Leon Simon, Theorems on Regularity and Singularity of Energy Minimizing Maps ,(1996)
Frank Duzaar, Joseph F. Grotowski, Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation Manuscripta Mathematica. ,vol. 103, pp. 267- 298 ,(2000) , 10.1007/S002290070007
Giuseppe Mingione, Regularity of minima: an invitation to the Dark Side of the Calculus of Variations Applications of Mathematics. ,vol. 51, pp. 355- 426 ,(2006) , 10.1007/S10778-006-0110-3
Claudia Capone, Luigi Greco, Tadeusz Iwaniec, Higher integrability via Riesz transforms and interpolation Nonlinear Analysis-theory Methods & Applications. ,vol. 49, pp. 513- 523 ,(2002) , 10.1016/S0362-546X(01)00119-5
Mariano Giaquinta, Giuseppe Modica, Almost-everywhere regularity results for solutions of non linear elliptic systems Manuscripta Mathematica. ,vol. 28, pp. 109- 158 ,(1979) , 10.1007/BF01647969
J.F. Grotowski, Boundary regularity for nonlinear elliptic systems Calculus of Variations and Partial Differential Equations. ,vol. 15, pp. 353- 388 ,(2002) , 10.1007/S005260100131