A Compact Course on Linear Pdes (Paperback, 2020)

1. Introduction.- 2. Second order linear elliptic equations.- 3. A bit of functional analysis.- 4. Weak derivatives and Sobolev spaces.- 5. Weak formulation of elliptic PDEs.- 6. Technical results.- 7. Additional results.- 8. Saddle points problems.- 9. Parabolic PDEs.- 10. Hyperbolic PDEs.- A Partition of unity.- B Lipschitz continuous and smooth domains.- C Integration by parts for smooth functions and vector ?elds.- D Reynolds transport theorem.- E Gronwall lemma.- F Necessary and su?cient conditions for the well-posedness of the variationalproblem.