Related papers: An elliptic inequality for nonlinear Hodge fields
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
The paper is devoted to investigating a Cauchy problem for nonlinear elliptic PDEs in the abstract Hilbert space. The problem is hardly solved by computation since it is severely ill-posed in the sense of Hadamard. We shall use a modified…
In this paper, we study the existence and regularity of solutions for a class of nonlinear singular elliptic equations involving unbounded coefficients and a singular right-hand side. Specifically, we are interested to problem whose…
A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville Theorem for general phase transition potentials. Gradient estimates are…
We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…
Following a recent paper by N. Mandache (Inverse Problems 17 (2001), pp. 1435-1444), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to many elliptic inverse problems…
In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -\Delta u+\frac{\mu}{|x|^2} u=u^p\quad {\rm in}\quad \Omega\setminus\{0\},\qquad…
Under a Morse index condition we prove symmetry results for solutions of a nonlinear mixed boundary condition elliptic problem. As an intermediate step we relate the Morse index of a solution to a mixed boundary condition linear eigenvalue…
In this paper, we establish a scale invariant Harnack inequality for some inhomogeneous parabolic equations in a suitable intrinsic geometry dictated by the nonlinearity. The class of equations that we consider correspond to the parabolic…
Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…
A refinement of the Hardy inequality has been presented by use of superquadratic function.
We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where constraining the values of the field to lie in a cone compensates…
A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.
We prove the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with homogeneous Neumann boundary conditions. This result complements our previous results obtained in [12], where the existence…
Comparison results for solutions to the Dirichlet problems for a class of nonlinear, anisotropic parabolic equations are established. These results are obtained through a semi-discretization method in time after providing estimates for…
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
We give H\"older's inequalities for integral and conditional expectation involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for the operator are established.
In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general…
In this manuscript we prove the existence of solutions to a fully nonlinear system of (degenerate) elliptic equations of Lane-Emden type and discuss a inhomogeneous generalization.
This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method the pointwise boundary H\"{o}lder regularity under proper…