1,721,018 research outputs found
Symmetry and convexity of level sets of solutions to
No full textWe consider the equation
−infinity-Laplacian(u) = f(u) in a domain Omega
with zero Dirichlet condition.
where f is a nonnegative continuous function. We investigate
whether the solutions to this equation inherit geometrical properties from the
domain. We obtain results concerning convexity of level sets and symmetry of solutions
Isolated singularities of solutions to the equation in the plane
No full textWe study the polar singularities of solutions to equations of the form in the plane. We assume a degenerate (and singular) ellipticity condition which includes the p-Laplacian as particular case. We represent the complex gradient of the solutions around a non-removable polar singularity in terms of a series expansion of a quasi conformal mapping H. The analysis of the asymptotic behavior of H gives power estimates from above and below for |Du| and we also obtain an upper bound for the index of Du in , depending on the rate of growth of |Du|
A lower bound for the gradient of -harmonic functions
No full textWe establish a lower bound for the gradient of the solution to infinity-Laplace equation
in a strongly star-shaped annulus with capacity type boundary conditions. The proof
involves properties of the radial derivative of the solution, so that starshapedness of level
sets easily follows
An approximate Gidas-Ni-Nirenberg theorem
No full textWe study positive solutions to in , on , and we address the following question: if is a small perturbation of a ball, is a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity and on the topologies in which perturbations are considered
The inverse conductivity problem with one measurement: bounds on the size of the unknown object
No full textSIAM J. APPL.MATH
Volume bounds of inclusions from physical EIT measurements
No full textWe derive estimates on the volume of an unknown inclusion in an electrically conducting body from current and voltage measurements at the boundary. We adopt the so-called complete model of electrical impedance tomography
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