2,848 research outputs found
Generalized Harnack inequality for semilinear elliptic equations
This paper is concerned with semilinear equations in divergence form
\diver(A(x)Du) = f(u) where is nondecreasing. We
prove a sharp Harnack type inequality for nonnegative solutions which is
closely connected to the classical Keller-Osserman condition for the existence
of entire solutions
Minimality via second variation for microphase separation of diblock copolymer melts
We consider a non local isoperimetric problem arising as the sharp interface
limit of the Ohta-Kawasaki free energy introduced to model microphase
separation of diblock copolymers. We perform a second order variational
analysis that allows us to provide a quantitative second order minimality
condition. We show that critical configurations with positive second variation
are indeed strict local minimizers of the nonlocal perimeter. Moreover we
provide, via a suitable quantitative inequality of isoperimetric type, an
estimate of the deviation from minimality for configurations close to the
minimum in the topology
Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality
We provide a full quantitative version of the Gaussian isoperimetric
inequality. Our estimate is independent of the dimension, sharp on the decay
rate with respect to the asymmetry and with optimal dependence on the mass
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