Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects
Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects
Abstract We study the following parabolic nonlocal 4-th order degenerate equation: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:msub> <m:mi>u</m:mi> <m:mi>t</m:mi> </m:msub> <m:mo>=</m:mo> <m:mrow> <m:mo>-</m:mo> <m:msub> <m:mrow> <m:mo maxsize="160%" minsize="160%">[</m:mo> <m:mrow> <m:mrow> <m:mn>2</m:mn> <m:mo></m:mo> <m:mi>π</m:mi> <m:mo></m:mo> <m:mi>H</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:msub> <m:mi>u</m:mi> <m:mi>x</m:mi> </m:msub> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi>ln</m:mi> <m:mo></m:mo> …