On the boundary this equation attains the value φ (p) ≡ g (p) where the point on the boundary has been distinguished by small p. Hence to solve Dirichlet's problem, one must find the value of σ (q) ...

Variational methods form a fundamental toolkit for analysing nonlinear elliptic equations by recasting boundary value problems as questions about critical points of suitably defined energy functionals ...

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our ...