Marco Discacciati, Claudia Garetto, Costas Loizou
Published 2022-08-06Version 1
This paper complements the study of the wave equation with discontinuous coefficients initiated in \cite{DGL:22} in the case of time-dependent coefficients. Here we assume that the equation coefficients are depending on space only and we formulate Levi conditions on the lower order terms to guarantee the existence of a very weak solution as defined in \cite{GR:14}. As a toy model we study the wave equation in conservative form with discontinuous velocity and we provide a qualitative analysis of the corresponding very weak solution via numerical methods.
Regularity theory and Green's function for elliptic equations with lower order terms in unbounded domains
On the Formation of Singularities in the Critical O(3) Sigma-Model
The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity
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