Sentence examples for uniqueness and regularity of from inspiring English sources

The existence, uniqueness and regularity of a weak solution is addressed.

By using only analytic tools we prove existence, uniqueness, and regularity of solutions.

A weak formulation is developed, the existence, uniqueness and regularity of the solutions are studied.

We first introduce a definition of a solution resembling Stampacchia's definition in the sense of duality and then, using the results of the first part, we prove the existence, uniqueness and regularity of solutions of the problem under mild assumptions on the data.

The author studied the existence, uniqueness, and regularity of solutions.

In [12], the existence, uniqueness, and regularity of solutions were obtained.

(2.2) For the special case where (a t,x equivfrac{c^{2}}{4}), namely for the doubly periodic problem of the linear telegraph equation u_{tt}-u_{xx}+c u_{t}+frac{c^{2}}{4} u=h t, x),quad mbox{in }mathcal {D}'bigl(mathbb{T}^{2} bigr), (2.3) the existence-uniqueness and regularity of solution have been discussed by Ortega and Robles-Perez in [15].

The existence, uniqueness, and the regularity of solutions of Euler equations are three popular research topics.

These problems for Schrödinger systems in domain with conical points are considered in [1], [2], in which authors consider the existence, the uniqueness and the regularity of solutions of the mentioned problems.

In addition, we investigate the associated quasi-linear elliptic problem with general Wentzell boundary conditions, and obtain existence, uniqueness and global regularity of weak solutions to this equation.

We prove existence, uniqueness and optimal regularity of solutions to the stationary obstacle problem defined by the fractional Laplacian operator with drift, in the subcritical regime.