Spherically Symmetric Solutions of an Elliptic-Parabolic Neumann Problem

The Regularity and Neumann Problem for Non-symmetric Elliptic Operators

We establish optimal Lp bounds for the non-tangential maximal function of the gradient of the solution to a second-order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the vertical variable, on the domain above a Lipschitz graph in the plane, in terms of the Lp-norm at the boundary of the tangential derivative of the Dirichlet d...

Spherically Symmetric Solutions in a New Braneworld Massive Gravity Theory

In this paper, a combination of the braneworld scenario and covariant de Rham-Gabadadze-Tolley (dRGT) massive Gravity theory is proposed. In this setup, the five-dimensional bulk graviton is considered to be massive. The five dimensional nonlinear ghost-free massive gravity theory affects the 3-brane dynamics and the gravitational potential on the brane. Following the solutions with spherical s...

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

An Asymptotic Analysis of Spherically Symmetric Perfect Fluid Similarity Solutions

The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p = αμ (−1 < α < 1) are described. We prove that for large and small values of the similarity variable, z = r/t, all such solutions must have an asymptotic power-law form. They are associated either with an exact power-law solution, in which case the α > 0 ones are asymptotically Fried...

Theory of General Conservation: Spherically Symmetric Solutions

A theory has been developed which extends the geometrical structure of a real four-dimensional space-time via a field of orthonormal tetrads with an enlarged transformation group. This new transformation group, called the conservation group, contains the group of diffeomorphisms as a proper subgroup and is the foundation of the theory of general conservation. Field equations for the free field ...