Boundary behavior and the Dirichlet problem for Beltrami equations

Boundary Integral Equations for the Laplace–Beltrami Operator

The Dirichlet Problem for Nonuniformly Elliptic Equations

and repeated indices indicate summation from 1 to n. The functions a'(x, u, p), a(x, u, p) are defined in QX£ n + 1 . If furthermore for any ikf>0, the ratio of the maximum to minimum eigenvalues of [a(Xy u, p)] is bounded in ÛX( — M, M)XE, Qu is called uniformly elliptic. A solution of the Dirichlet problem Qu = Q, u—<f)(x) on <50 is a C(n)P\C(O) function u(x) satisfying Qu = 0 in £2 and agree...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...