The free boundary of a semilinear elliptic equation
The free boundary of a semilinear elliptic equation
The Dirichlet problem <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Delta u equals lamda f left-parenthesis u right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="normal">Δ<!-- Δ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>λ<!-- λ --></mml:mi> <mml:mspace width="thinmathspace" /> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\Delta u = \lambda \,f(u)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in a domain …