Related papers: The two membranes problem in a regular tree
The problem of the exact bounded control of oscillations of the two-dimensional wave equation is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…
We study the extreme local structure of plane binary trees through the distribution of leaves at maximum depth. We first address two basic questions: (i) the asymptotic probability that exactly two leaves occur at the deepest level, and…
In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…
The aim of this paper is analyzing existence, multiplicity, and regularity issues for the positive solutions of a Neumann boundary value problem of superlinear indefinite type related to the mean curvature operator with a sublinear…
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…
The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…
We study multiport networks, common in electrical engineering. They have boundary conditions different from electrical networks: the boundary vertices are split into pairs and the sum of the incoming currents is set to be zero in each pair.…
The structures in target space geometry that correspond to conformally invariant boundary conditions in WZW theories are determined both by studying the scattering of closed string states and by investigating the algebra of open string…
We present results of existence, regularity and uniqueness of solutions of the master equation associated with the mean field planning problem in the finite state space case, in the presence of a common noise. The results hold under…
Scattering equations for tree-level amplitudes are viewed in the context of string theory. As a result of the comparison we are led to define a new dual model which coincides with string theory in both the small and large $\alpha'$ limit,…
We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under…
The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a…
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady state formulation amounts to recasting the nonlinear problem as…
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
In this paper we continue the study started in part I (posted). We consider a planar, bounded, $m$-connected region $\Omega$, and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$ be a cellular decomposition of $\Omega\cup\bord\Omega$,…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
We develop algorithms, implemented in Maple, that study the number of vertices with a particular number of children in a random ordered tree where all vertices must have a number of children in some finite set. By calculating the mixed…
New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate…