齐次群上次椭圆超抛物障碍问题的Caccioppoli不等式和高阶可积性

Caccioppoli inequality and higher integrability for the subelliptic ultraparabolic obstacle problems on the homogeneous group

通过构造合适的试验函数,建立弱解的表示公式,并利用奇异积分估计证明齐次群上一类二阶非线性次椭圆超抛物方程障碍问题弱解的Caccioppoli不等式和高阶可积性结果.推广了欧氏空间中超抛物障碍问题的相应结果.

By constructing the suitable test function,establishing the representation formula for the weak solution and using estimates of singular integrals,a Caccioppoli inequality and higher integrability for weak solutions to the obstacle problems related to a class of second order nonlinear subelliptic ultraparabolic equations on the homogeneous group are obtained.These results are generalized the corresponding conclusions of ultraparabolic obstacle problems in the Euclidean case.