TY - JOUR
T1 - Some interior regularity results for solutions of Hessian equations
AU - Urbas, John
PY - 2000/8
Y1 - 2000/8
N2 - We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution. In the special case k = 2 we deduce that weak solutions in W2,p(Ω), p > n - 1, have locally Hölder continuous gradients. In the nondegenerate case we also show that weak solutions in W2,p(Ω), p > kn/2, have locally bounded second derivatives.
AB - We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution. In the special case k = 2 we deduce that weak solutions in W2,p(Ω), p > n - 1, have locally Hölder continuous gradients. In the nondegenerate case we also show that weak solutions in W2,p(Ω), p > kn/2, have locally bounded second derivatives.
UR - http://www.scopus.com/inward/record.url?scp=0013090015&partnerID=8YFLogxK
U2 - 10.1007/s005260050001
DO - 10.1007/s005260050001
M3 - Article
SN - 0944-2669
VL - 11
SP - 1
EP - 31
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
ER -