L p $L^{p}$ -Estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth

Bang-Cheng Sun, Zhi-Ming Liu, Qiang Li, Shen-Zhou Zheng
2016 Boundary Value Problems  
We prove an interior L p -estimate of X-gradient of weak solutions to a class of quasilinear subelliptic equations with VMO coefficients under controllable growth. Here, we use a reverse Hölder inequality and De Giorgi's iteration to establish the boundedness of their weak solutions. Then a local L p -estimate of the X-gradient of the weak solutions is derived by way of the bootstrap argument. MSC: 35J50; 35J47
doi:10.1186/s13661-016-0658-8 fatcat:cyokyb5r25eq7m6jtimntcuueq