Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients
Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients
Abstract In this paper, we study the degenerate parabolic system $$ u_{t}^{i} + X_{\alpha }^{*} \bigl(a_{ij}^{\alpha \beta }(z){X_{\beta }} {u^{j}}\bigr) = {g_{i}}(z,u,Xu) + X_{\alpha }^{*} f_{i}^{\alpha }(z,u,Xu), $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>u</mml:mi> <mml:mi>t</mml:mi> <mml:mi>i</mml:mi> </mml:msubsup> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mi>X</mml:mi> <mml:mi>α</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mrow> <mml:mi>i</mml:mi> <mml:mi>j</mml:mi> </mml:mrow> <mml:mrow> …