In this paper we investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain – including a very weak compatibility condition between the Dirichlet boundary part and its complement – we prove Hölder continuity of the solu...

[1] Simulations of mixed-phase clouds in forecasts with the NCAR Atmosphere Model version 3 (CAM3) and the GFDL Atmospheric Model version 2 (AM2) for the MixedPhase Arctic Cloud Experiment (M-PACE) are performed using analysis data from numerical weather prediction centers. CAM3 significantly underestimates the observed boundary layer mixed-phase cloud fraction and cannot realistically simulate...

We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE(κ, ρ) theories. We derive a set of conditions connecting the total charge of the coulomb gas, the boundary charges, the parameters κ and ρ. Also we study a free fermion theory in presence of a boundary and show with the same methods that i...

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian primary constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. We discuss the Dirac brackets and the reduced phase space structure for different boundary conditio...

We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and viceversa. The switching occurs both in time and in different portions of the boundary. For this problem, we apply and extend the Nitsche’s method presented in [Jun...

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian primary constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. We discuss the Dirac brackets and the reduced phase space structure for different boundary conditio...

We consider the free fall of a sphere above a wall in a viscous incompressible fluid. Weinvestigate the influence of boundary conditions on the finite-time occurrence of contactbetween the sphere and the wall. We prove that slip boundary conditions enable tocircumvent the ”no-collision” paradox associated with no-slip boundary conditions. Wealso examine the case of mixed bou...

This paper describes existence, uniqueness and special eigenfunction representations of H1−solutions of second order, self-adjoint, elliptic equations with both interior and boundary source terms. The equations are posed on bounded regions with Dirichlet conditions on part of the boundary and Neumann conditions on the complement. The system is decomposed into separate problems defined on orthog...