Regularity for Quasi-Linear <i<p</i<-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group

When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</m...
Ausführliche Beschreibung

When <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mn<2</mn<<mo<−</mo<<mn<1</mn<<mo</</mo<<mi<Q</mi<<mo<<</mo<<mi<p</mi<<mo<≤</mo<<mn<2</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<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<0</mn<<mo<,</mo<<mn<1</mn<</mrow<</msubsup<</semantics<</math<</inline-formula< and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msubsup<<mi<C</mi<<mrow<<mspace width="0.166667em"<</mspace<<mi<loc</mi<<mspace width="0.166667em"<</mspace<</mrow<<mrow<<mn<1</mn<<mo<,</mo<<mi<α</mi<</mrow<</msubsup<</semantics<</math<</inline-formula<-regularities of weak solutions to quasi-linear <i<p</i<-Laplacian type non-homogeneous equations in 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<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<Q</mi<<mo<=</mo<<mn<2</mn<<mi<n</mi<<mo<+</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< is the homogeneous dimension of <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<. Ausführliche Beschreibung