We give a survey at an introductory level of old and recent results in the study of critical
points of solutions of elliptic and parabolic partial differential equations. To keep the …

We investigate the location of the (unique) hot spot in a convex heat conductor with uniform
initial temperature and with boundary grounded at zero temperature. We present two …

We establish a relationship between stationary isothermic surfaces and uniformly dense
domains. A stationary isothermic surface is a level surface of temperature which does not …

We consider the solution u of ut− Δ p G u= 0 in a (not necessarily bounded) domain Ω, such
that u= 0 in Ω at time t= 0 and u= 1 on the boundary of Ω at all times. Here, Δ p G is the game …

We investigate a potential with a radially symmetric and strictly decreasing kernel depending
on a parameter. We regard the potential as a function defined on the upper half-space …

We consider a convex polygonal heat conductor whose inscribed circle touches every side
of the conductor. Initially, the conductor has constant temperature and, at every time, the …

The object of our investigation is a point that gives the maximum value of a potential with a
strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we …

We consider the (viscosity) solution $ u (x, t) $ of the nonlinear evolution equation $ u_t-
\Delta^ G_p u= 0$ in a (not necessarily bounded) domain $\Omega $, such that $ u= 0$ in …

We analytically characterize equilateral triangles. Our characterization includes the
classically well-known characterizations: for a given triangle in the Euclidean plane, if the …

We investigate a potential obtained as the convolution of a radially symmetric function and
the characteristic function of a body (the closure of a bonded open set) with exterior cones …