Borderline Lipschitz regularity for bounded minimizers of functionals with (<i>p</i>,<i>q</i>)-growth
Borderline Lipschitz regularity for bounded minimizers of functionals with (<i>p</i>,<i>q</i>)-growth
Abstract We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>p</m:mi> <m:mo>,</m:mo> <m:mi>q</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(p,q)} -growth with the source term in the Lorentz space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>L</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>N</m:mi> <m:mo>,</m:mo> <m:mn>1</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> …