Regularity of Weak Solutions
It is shown that under appropriate ellipticity assumptions, weak solutions of partial differential equations (PDEs) are smooth. This applies in particular to the Laplace equation for harmonic functions, thereby justifying Dirichlet’s principle introduced in the previous paragraph.
KeywordsWeak Solution Schwarz Inequality Weak Equation Difference Quotient Sobolev Embedding Theorem
Unable to display preview. Download preview PDF.