Related papers: Exterior Dirichlet problem for Hessian equations o…
An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting…
In this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple…
We prove new existence and uniqueness results in full Sobolev spaces for the steady-state Oseen problem in a smooth exterior domain of $\mathbb{R}^n$, $n\ge 2$. These results are then employed, on the one hand, in the study of analogous…
We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. For axially symmetric domains we prove that, under suitable assumptions, there exist Mountain-pass solutions which exhibit partial symmetry. Furthermore, we show…
In this note we study the boundary regularity of solutions to nonlocal Dirichlet problems of the form $Lu=0$ in $\Omega$, $u=g$ in $\mathbb R^N\setminus\Omega$, in non-smooth domains $\Omega$. When $g$ is smooth enough, then it is easy to…
We present an announcement of some recent results concerning well-posedness of the Poisson-Dirichlet problem with boundary data in Besov spaces with fractional smoothness. This is a far-reaching generalization as previously known theorems…
We consider a helicoidal group $G$ in $\mathbb{R}^{n+1}$ and unbounded $G$-invariant $C^{2,\alpha}$-domains $\Omega\subset\mathbb{R}^{n+1}$ whose helicoidal projections are exterior domains in $\mathbb{R}^{n}$, $n\geq2$. We show that for…
We derive a priori estimates for second order derivatives of solutions to a wide calss of fully nonlinear elliptic equations on Riemannian manifolds. The equations we consider naturally appear in geometric problems and other applications…
We prove that, in a $m$-hyperconvex domain in $\mathbb{C}^{n},$ if a non-negative Borel measure is dominated by a complex Hessian measure, then it is a complex Hessian measure of a function in the class $\mathcal{N}_m(H)$. This is an…
We study the variational problem for $N$-parallel curves on a Finslerian surface by means of Exterior Differential Systems using Griffiths' method. We obtain the conditions when these curves are extremals of a length functional and write…
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is…
The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three dimensional manifolds. We introduce two numerical methods for this PDE: the first is provably…
In this paper, we study Hessian equations and complex quotient equations on closed Hermitian manifolds. We directly derive the uniform estimate for the admissible solution. As an application, we solve general Hessian equations on closed…
In this paper, we prove new rigidity results related to some generalised Ricci-Hessian equation on Riemannian manifolds.
We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $\Omega \subseteq \mathbb{R}^n$. Specifically, we show that if…
In this paper, two new results and short proofs are given for the existence of positive entire large and bounded radial positive solutions for a nonlinear system with gradient term. Our results complete and improve a recently work published…
In this paper, we study the Dirichlet problem for the implicit degen- erate nonlinear elliptic equation with variable exponent in a bounded domain. We obtain sufficient conditions for the existence of a solution with- out regularization and…
In this paper, we solve the Dirichlet problem with continuous boundary data for the Lagrangian mean curvature equation on a uniformly convex, bounded domain in $\mathbb{R}^n$.
We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are H\"{o}lder continuous and that may have infinite Dirichlet integral. We introduce a distributional normal derivative on the boundary…