97 research outputs found
Rellich inequalities with weights
Let be a cone in with . For every fixed
we find the best constant in the Rellich inequality
for . We also estimate the best constant for
the same inequality on . Moreover we show improved Rellich
inequalities with remainder terms involving logarithmic weights on cone-like
domains
Rellich inequalities with weights
Let be a cone in with . For every fixed
we find the best constant in the Rellich inequality
for . We also estimate the best constant for
the same inequality on . Moreover we show improved Rellich
inequalities with remainder terms involving logarithmic weights on cone-like
domains
Isovolumetric and isoperimetric problems for a class of capillarity functionals
Capillarity functionals are parameter invariant functionals defined on
classes of two-dimensionals parametric surfaces in R3 as the sum of the area
integral with an anisotropic term of suitable form. In the class of parametric
surfaces with the topological type of S2 and with fixed volume, extremals of
capillarity functionals are surfaces whose mean curvature is prescribed up to a
constant. For a certain class of anisotropies vanishing at infinity, we prove
existence and nonexistence of volume- constrained, S2-type, minimal surfaces
for the corresponding capillarity functionals. Moreover, in some cases, we show
existence of extremals for the full isoperimetric inequality.Comment: 27 page
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