$$H^2$$-regularity of Steklov eigenfunctions on convex domains via Rellich-Pohozaev identity

Abstract

<jats:p> We prove that the Steklov eigenfunctions on convex domains of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$\mathbb {R}^n$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> </jats:alternatives> </jats:inline-formula> are <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$H^2$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> </jats:alternatives> </jats:inline-formula> regular by adapting a classical argument combined with the Rellich-Pohozaev identity. </jats:p>