On a conjecture relative to the maximum of harmonic functions on convex domains: Unbounded domains.
On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity
In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation.
On a coupled problem between the plate equation and the membrane equation on polygons
On a critical threshold for nonlinear diffusion equations.
We study some aspects of the asymptotic behavior of the solutions to a class of nonlinear parabolic equations.
On a familiy of torsional creep problems.
On a fourth order superlinear elliptic problem.
On a free boundary problem for minimal surfaces.
On a general class of elliptic equations in devergence.
On a generalization of the Dirichlet integral.
On a generalization of the Keldysh theorem.
On a generalized reflection law for functions satisfying the Helmholtz equation.
On a ground state and two symmetric ground state solutions in a domain
On a hierarchical basis multilevel method with nonconforming P1 elements.
On a inequality of Friedrichs.
On a linear second order degenerate elliptic equation.
On a Liouville phenomenon for entire weak supersolutions of elliptic partial differential equations
On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two
In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in . We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.
On a local Lipschitz constant of the maps related to -decomposition.
On a magnetic characterization of spectral minimal partitions
Given a bounded open set in (or in a Riemannian manifold) and a partition of by open sets , we consider the quantity where is the ground state energy of the Dirichlet realization of the Laplacian in . If we denote by the infimum over all the -partitions of , a minimal -partition is then a partition which realizes the infimum. When , we find the two nodal domains of a second eigenfunction, but the analysis of higher ’s is non trivial and quite interesting. In this paper, we give...
On a maximum principle for elliptic systems with constant coefficients