Related papers: Singular Solution to Special Lagrangian Equations
This is the second of three papers math.DG/0111324, math.DG/0204343 studying special Lagrangian 3-submanifolds (SL 3-folds) N in C^3 invariant under the U(1)-action (z_1,z_2,z_3) --> (gz_1,g^{-1}z_2,z_3) for unit complex numbers g, using…
We prove the uniqueness of crepant resolutions for some quotient singularities and for some nilpotent orbits. The finiteness of non-isomorphic symplectic resolutions for 4-dimenensional symplectic singularities is proved. We also give an…
In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian…
We prove that outside of a closed singular set of measure zero solutions to the second boundary value problem for generated Jacobian equations are smooth.
Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which…
All $(-1)$-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a…
In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
We establish the equivalence between weak and viscosity solutions for non-homogeneous $p(x)$-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution…
A Lagrangian system with singularities is considered. The configuration space is a non-compact manifold that depends on time. A set of periodic solutions has been found.
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
It is proved the existence of nonclassical solutions of the Neumann and Poincare problems for generalizations of the Laplace equation in anisotropic and nonhomogeneous media in almost smooth domains with arbitrary boundary data that are…
This article develops optimality conditions for a large class of non-smooth variational models. The main results are based on standard tools of functional analysis and calculus of variations. Firstly we address a model with equality…
In this paper we prove the existence and uniqueness of a solution to the nonstationary two dimensional system of equations describing miscible liquids with nonsmooth, multivalued and nonmonotone boundary conditions of subdifferential type.…
For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of…
We consider a class of fully non-linear parabolic equations on compact Hermitian manifolds involving symmetric functions of partial Laplacians. Under fairly general assumptions, we show the long time existence and convergence of solutions.…
In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
In this paper we construct explicit examples that show the sublevel sets of the solution of a $k$-Hessian equation defined on a convex ring do not have to be convex.