2022/04/27 by Wolfgang Arendt, Arendt, Wolfgang, Manfred Sauter +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2204.12981
We use form methods to define suitable realisations of the Laplacian on a domain Ω with Wentzell boundary conditions, i.e. such that ∂nu + βu + Δu = 0 holds in a suitable sense on the boundary of Ω. For those realisations, we study their semigroup generation properties. Using the approximative trace, we give a unified treatment that in part allows irregular and even fractal domains. Moreover, we admit β to be merely essentially bounded and complex-valued. If the domain is Lipschitz, we obtain a kernel continuous up to the boundary.