Bilateral Evolution Problems of Non-Variational Type: Existence, Uniqueness, Hölder-Regularity and Approximation of Solutions.
Blow-up of nonnegative solutions to quasilinear parabolic inequalities
We investigate critical exponents for blow-up of nonnegative solutions to a class of parabolic inequalities. The proofs make use of a priori estimates of solutions combined with a simple scaling argument.
Blow-up results for nonlinear hyperbolic inequalities
Boundary trace of positive solutions of nonlinear elliptic inequalities
We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of in a smooth domain under very general assumptions on . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the nonlinearity...