The dynamics of acceleration of electrons in a gas diode in a sharply inhomogeneous electric field due to the configuration of electrodes is studied. For the edge cathode based on the analytical solution of the equations of motion of electrons, it is shown that their acceleration at the periphery, in the weak field, is possible only if the applied potential difference exceeds a certain threshold value determined by the interelectrode distance and gas parameters. This condition complements the classical condition of escape, according to which the electric field strength at the edge of the cathode should exceed the value dependent only on the gas parameters. According to estimates, the new condition imposes higher requirements than the classical one on the field value in the limit of the strongly pointed cathode edge.