Related papers: Elliptic Equations Involving Meausres
This work proposes to generalize certain results regarding some semilinear elliptic systems.
An optimal control problem governed by semilinear elliptic partial differential equations is considered. The equation is in divergence form with the leading term containing controls. By studying the $G$-closure of the leading term, an…
We study certain typical semilinear elliptic equations in Euclidean space $\bR^{n}$ or on a closed manifold $M$ with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method.…
We will present some rigidity results for solutions to semilinear elliptic equations of the form $\Deltau = W'(u)$, where W is a quite general potential with a local minimum and a local maximum. We are particularly interested in…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
For a semilinear elliptic equation, we prove uniqueness results in determining potentials and semilinear terms from partial Cauchy data on an arbitrary subboundary.
By using truncation technique, minimization method and Morse theory, we obtain three nontrivial solutions for a class of semilinear elliptic equations.
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming…
We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory,…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
We revisit the regularity theory for uniformly elliptic equations.
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
In this paper, we prove some pointwise comparison results between the solutions of some second-order semilinear elliptic equations in a domain $\Omega$ of $\R^n$ and the solutions of some radially symmetric equations in the equimeasurable…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.