Find in Library

In this article, when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mn>4</mn></mrow></semantics></math></inline-formula>, we establish the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>C</mi><mrow><mi>loc</mi></mrow><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></msubsup></semantics></math></inline-formula>-regularity of weak solutions to the degenerate parabolic <i>p</i>-Laplacian equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>∂</mo><mi>t</mi></msub><mi>u</mi><mo>=</mo><mo>−</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover></mstyle><msubsup><mi>X</mi><mi>i</mi><mo>*</mo></msubsup><mrow><mo>(</mo><mo stretchy="false">|</mo></mrow><mrow><msub><mo>∇</mo><mi mathvariant="script">H</mi></msub><mi>u</mi></mrow><mrow><msup><mo stretchy="false">|</mo><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><msub><mi>X</mi><mi>i</mi></msub><mi>u</mi><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> on the group SU(3) granted with horizontal vector fields <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>X</mi><mn>1</mn></msub><mo>,</mo><mo> </mo><mo>…</mo><mo>,</mo><mo> </mo><msub><mi>X</mi><mn>6</mn></msub></mrow></semantics></math></inline-formula>. Compared to the Heisenberg group, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">H</mi></mrow><mi>n</mi></msup></semantics></math></inline-formula>, we obtained the optimal range of <i>p</i>; that is, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mn>4</mn></mrow></semantics></math></inline-formula>.