An elliptic semilinear equation with source term and boundary measure data: The supercritical case

作者：Bidaut Veron Marie Francoise; Hoang Giang; Quoc Hung Nguyen; Veron Laurent^*

来源：Journal of Functional Analysis, 2015, 269(7): 1995-2017.

DOI：10.1016/j.jfa.2015.06.020

• Riesz potentials
• Hardy potentials
• Quasi-metric
• Capacities

We give new criteria for the existence of weak solutions to an equation with a super linear source term
-Delta u = u(q) in Omega, u = sigma on partial derivative Omega
where Omega is either a bounded smooth domain or R-+(N), q > 1 and sigma is an element of m(+)(partial derivative Omega) is a nonnegative Radon measure on partial derivative Omega. One of the criteria we obtain is expressed in terms of some Bessel capacities on partial derivative Omega. We also give a sufficient condition for the existence of weak solutions to equation with source mixed terms.
-Delta u = vertical bar u vertical bar(q1-1)u vertical bar del u vertical bar(q2) in Omega, u = sigma on partial derivative Omega
where q(1), q(2) >= 0, q(1) + q(2) >1, q(2) < 2, sigma is an element of m(partial derivative Omega) is a Radon measure on partial derivative Omega.

• 出版日期2015-10-1