Initial value problems for diffusion equations with singular potential

Our main result in the present paper is the proof of the uniform in time strong convergence in L p ( Ω ), p < +∞, of the approximate solution given by the finite volume

In the same sense any positive bounded Radon measure ν cannot be the regular part of the initial trace of a positive solution of (1.26) since condition (1.15) is equivalent to p <

and V´eron L., Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case arXiv:0907.1006v3, submitted. [21]

solutions with kδ 0 as initial data and the behaviour of these solutions when k → ∞; (b) the existence of an initial trace and its properties; (c) uniqueness and non-uniqueness

In order to characterize positive good measures, we introduce a framework of nonlinear analysis which have been used by Dynkin and Kuznetsov (see [16] and references therein) and

Relaxed formulation for the Steklov eigenvalues: existence of optimal shapes In this section we extend the notion of the Steklov eigenvalues to arbitrary sets of finite perime- ter,

Section 5 will be devoted to the proof of the local existence and the existence of weak solutions under some weaker conditions to the initial function u

Local existence and uniqueness theory for the inverted profile equation The purpose of this section is to prove an existence and uniqueness theorem for solutions of (1.12) on