For a rounded rectangle you can do it all in XAML using radial gradients for the corners and linear gradients for the sides.
The example uses a ViewBox so the Size doesn't need to be set both on the grid and its clip path. If you need it to resize keeping the same border radius you could bind RectangleGeometry.Rect and use a ValueConverter. The gradient and the RadiusX and RadiusY properties can be easily changed in one place.
<Viewbox Stretch="Fill">
<Grid Width="100" Height="100">
<Grid.Resources>
<Color x:Key="inside">White</Color>
<GradientStopCollection x:Key="gradient">
<GradientStop Color="Black" Offset="1"/>
<GradientStop Color="{DynamicResource inside}" Offset="0.2"/>
</GradientStopCollection>
</Grid.Resources>
<Grid.Clip>
<RectangleGeometry RadiusX="15" RadiusY="30" Rect="0,0,100,100" x:Name="clip" />
</Grid.Clip>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="{Binding RadiusX, ElementName=clip}" />
<ColumnDefinition Width="1*"/>
<ColumnDefinition Width="{Binding RadiusX, ElementName=clip}" />
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition Height="{Binding RadiusY, ElementName=clip}"/>
<RowDefinition Height="1*"/>
<RowDefinition Height="{Binding RadiusY, ElementName=clip}"/>
</Grid.RowDefinitions>
<Rectangle Grid.Column="1" Margin="-1,0">
<Rectangle.Fill>
<LinearGradientBrush EndPoint="0,0" MappingMode="RelativeToBoundingBox" StartPoint="0,1" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Column="2" Grid.Row="1" Margin="0,-1">
<Rectangle.Fill>
<LinearGradientBrush EndPoint="1,0" MappingMode="RelativeToBoundingBox" StartPoint="0,0" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Column="1" Grid.Row="2" Margin="-1,0">
<Rectangle.Fill>
<LinearGradientBrush EndPoint="0.5,1" MappingMode="RelativeToBoundingBox" StartPoint="0.5,0" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Row="1" Margin="0,-1">
<Rectangle.Fill>
<LinearGradientBrush EndPoint="0,0" MappingMode="RelativeToBoundingBox" StartPoint="1,0" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Column="1" Grid.Row="1" Margin="-1">
<Rectangle.Fill>
<SolidColorBrush Color="{DynamicResource inside}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle>
<Rectangle.Fill>
<RadialGradientBrush Center="1,1" RadiusX="1" RadiusY="1" GradientOrigin="1,1" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Column="2">
<Rectangle.Fill>
<RadialGradientBrush Center="0,1" RadiusX="1" RadiusY="1" GradientOrigin="0,1" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Column="2" Grid.Row="2">
<Rectangle.Fill>
<RadialGradientBrush Center="0,0" RadiusX="1" RadiusY="1" GradientOrigin="0,0" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
<Rectangle Grid.Row="2">
<Rectangle.Fill>
<RadialGradientBrush Center="1,0" RadiusX="1" RadiusY="1" GradientOrigin="1,0" GradientStops="{DynamicResource gradient}" />
</Rectangle.Fill>
</Rectangle>
</Grid>
</Viewbox>
If you need to a gradient to follow more complex shapes you can do it with a V3.0 PixelShader.