相关论文: Quantitative results for fractional overdetermined…

We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. The extension of the result…

We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity…

We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider…

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove…

We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.

In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of…

We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…

We prove the Harnack inequality for antisymmetric $s$-harmonic functions, and more generally for solutions of fractional equations with zero-th order terms, in a general domain. This may be used in conjunction with the method of moving…

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…

We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function $P$ and integral identities. In dimension…

In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap…

We establish two new estimates which control a function (after subtracting its average) in $L^1$ by only the $L^1$ norm of its radial derivative. While the interior estimate holds for all superharmonic functions, the boundary version is…

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…

We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

In this paper, we consider an unconventional overdetermined problem through a property of concavity, which provides some characterizations of balls via Brunn-Minkowski inequalities. In this setting, our rsults can be viewed as the…

We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes…

One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…