Nonlinear elliptic equations with measure valued absorption potentials

In the general case, assuming that Ω possesses a tangent cone at every boundary point and q is subcritical, we prove an existence and uniqueness result for positive solutions

so that high resolution can be obtained by employing narrow linewidth continuous-wave (CW) lasers. In addition, the difference between the frequencies of the pump and probe beams can

Gallo, The Cauchy Problem for defocusing Nonlinear Schr¨odinger equations with non- vanishing initial data at infinity, preprint..

Intuitively, wherever the gradient of a function u is small, the function will be Lipschitz, so we should not need any further information from the equation at those points in order

It is also very useful when we make a systematic analysis of the gradients of solutions of nonlinear elliptic and parabolic problems near the boundary of the irregular domain which

Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case.. M OSHE M ARCUS AND L AURENT

sequence in the Sobolev Space and hence the existence of weak solutions provided uniform L °° -bounds are available depending on the maximal.. angle between the

Rakotoson (Quasilinear elliptic problems with measures as data, Differential Integral Equations.. 4 (1991), 449-457) and by Boccardo and Gallouet (Nonlinear