We consider Calderón’s inverse problem on planar domains Ω with conductivities in fractional Sobolev spaces. When Ω is Lipschitz, the problem was shown to be stable in the L–sense in [18]. We remove the Lipschitz condition on the boundary. To this end, we analyse the Sobolev regularity of the characteristic function of Ω. For Ω a quasiball, we compute ‖χΩ‖W s,p(Rd) in terms of the δ–neighbourho...

We present a semilocal convergence analysis for a simplified NewtonLavrentiev regularization method for solving ill-posed problems in a Hilbert space setting. We use a center-Lipschitz instead of a Lipschitz condition in our convergence analysis. This way we obtain: weaker convergence criteria, tighter error bounds and more precise information on the location of the solution than in earlier stu...

We show that local minimizers of functionals of the form Z Ω [f(Du(x)) + g(x , u(x))] dx, u ∈ u0 + W 1,p 0 (Ω), are locally Lipschitz continuous provided f is a convex function with p − q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.

In this Note, assuming that the generator is uniform Lipschitz in the unknown variables, we relate the solution of a one dimensional backward stochastic differential equation with the value process of a stochastic differential game. Under a domination condition, an Fconsistent evaluations is also related to a stochastic differential game. This relation comes out of a min-max representation for ...

A global optimization problem is studied where the objective function f(x) is a multidimensional black-box function and its gradient f ′(x) satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant K. Different methods for solving this problem by using an a priori given estimate of K, its adaptive estimates, and adaptive estimates of local Lipschitz constants are...

We show differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally antiLipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably...

In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...

We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore we discuss the relations of such a Bloch type condition with the analogous hyperbolic Lipschitz condition.

In [17], the author proved the existence and the uniqueness of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition when the generator and the terminal condition are locally Lipschitz. In this paper, we prove that the existence result remains true for these BSDEs when the regularity assumptions on the terminal condition is weakened.

In this paper, we study the existence and uniqueness of solutions to stochastic equations in innnite dimension with an integral-Lipschitz condition for the coeecients.